How to find the volume of a pyramid - PSAT Math

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Question

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

Answer

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

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Question

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Answer

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

Compare your answer with the correct one above

Question

What is the approximate volume of a square pyramid with one edge of the base measuring $2.7\textup{inches}$ and a height equal to the diagonal of its base?

Answer

If one edge of the base is 2.7 inches, and the height of the pyramid is equal to the diagonal of the base, we can find the height using the edge. The height is going to be equal to $\sqrt{2.7^2+2.7^2}=\sqrt{14.58}$ . The area of the base is . Volume of a pyramid is equal to $\left ( \frac{1}{3} \right )\left ( \textup{area of the base} \right )\left ( \textup{height} \right )$

This leaves us with

$v=(7.29)(\sqrt{14.58})\left ( \frac{1}{3} \right )\approx9.28$

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Question

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

Answer

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Compare your answer with the correct one above

Question

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Answer

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

Compare your answer with the correct one above

Question

What is the approximate volume of a square pyramid with one edge of the base measuring $2.7\textup{inches}$ and a height equal to the diagonal of its base?

Answer

If one edge of the base is 2.7 inches, and the height of the pyramid is equal to the diagonal of the base, we can find the height using the edge. The height is going to be equal to $\sqrt{2.7^2+2.7^2}=\sqrt{14.58}$ . The area of the base is . Volume of a pyramid is equal to $\left ( \frac{1}{3} \right )\left ( \textup{area of the base} \right )\left ( \textup{height} \right )$

This leaves us with

$v=(7.29)(\sqrt{14.58})\left ( \frac{1}{3} \right )\approx9.28$

Compare your answer with the correct one above

Question

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

Answer

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Compare your answer with the correct one above

Question

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Answer

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

Compare your answer with the correct one above

Question

What is the approximate volume of a square pyramid with one edge of the base measuring $2.7\textup{inches}$ and a height equal to the diagonal of its base?

Answer

If one edge of the base is 2.7 inches, and the height of the pyramid is equal to the diagonal of the base, we can find the height using the edge. The height is going to be equal to $\sqrt{2.7^2+2.7^2}=\sqrt{14.58}$ . The area of the base is . Volume of a pyramid is equal to $\left ( \frac{1}{3} \right )\left ( \textup{area of the base} \right )\left ( \textup{height} \right )$

This leaves us with

$v=(7.29)(\sqrt{14.58})\left ( \frac{1}{3} \right )\approx9.28$

Compare your answer with the correct one above

Question

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

Answer

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Compare your answer with the correct one above

Question

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Answer

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

Compare your answer with the correct one above

Question

What is the approximate volume of a square pyramid with one edge of the base measuring $2.7\textup{inches}$ and a height equal to the diagonal of its base?

Answer

If one edge of the base is 2.7 inches, and the height of the pyramid is equal to the diagonal of the base, we can find the height using the edge. The height is going to be equal to $\sqrt{2.7^2+2.7^2}=\sqrt{14.58}$ . The area of the base is . Volume of a pyramid is equal to $\left ( \frac{1}{3} \right )\left ( \textup{area of the base} \right )\left ( \textup{height} \right )$

This leaves us with

$v=(7.29)(\sqrt{14.58})\left ( \frac{1}{3} \right )\approx9.28$

Compare your answer with the correct one above

Question

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

Answer

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Compare your answer with the correct one above

Question

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Answer

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

Compare your answer with the correct one above

Question

What is the approximate volume of a square pyramid with one edge of the base measuring $2.7\textup{inches}$ and a height equal to the diagonal of its base?

Answer

If one edge of the base is 2.7 inches, and the height of the pyramid is equal to the diagonal of the base, we can find the height using the edge. The height is going to be equal to $\sqrt{2.7^2+2.7^2}=\sqrt{14.58}$ . The area of the base is . Volume of a pyramid is equal to $\left ( \frac{1}{3} \right )\left ( \textup{area of the base} \right )\left ( \textup{height} \right )$

This leaves us with

$v=(7.29)(\sqrt{14.58})\left ( \frac{1}{3} \right )\approx9.28$

Compare your answer with the correct one above

Question

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

Answer

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Compare your answer with the correct one above

Question

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Answer

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

Compare your answer with the correct one above

Question

What is the approximate volume of a square pyramid with one edge of the base measuring $2.7\textup{inches}$ and a height equal to the diagonal of its base?

Answer

If one edge of the base is 2.7 inches, and the height of the pyramid is equal to the diagonal of the base, we can find the height using the edge. The height is going to be equal to $\sqrt{2.7^2+2.7^2}=\sqrt{14.58}$ . The area of the base is . Volume of a pyramid is equal to $\left ( \frac{1}{3} \right )\left ( \textup{area of the base} \right )\left ( \textup{height} \right )$

This leaves us with

$v=(7.29)(\sqrt{14.58})\left ( \frac{1}{3} \right )\approx9.28$

Compare your answer with the correct one above

Question

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

Answer

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Compare your answer with the correct one above

Question

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Answer

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

Compare your answer with the correct one above

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How to find the volume of a pyramid - PSAT Math

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters. Since the base is a square, the area of the base is 3 x 3 = 9. Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Volume of a pyramid is Thus: Area of the base is . Therefore, each side is .

What is the approximate volume of a square pyramid with one edge of the base measuring and a height equal to the diagonal of its base?

If one edge of the base is 2.7 inches, and the height of the pyramid is equal to the diagonal of the base, we can find the height using the edge. The height is going to be equal to . The area of the base is . Volume of a pyramid is equal to This leaves us with

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters. Since the base is a square, the area of the base is 3 x 3 = 9. Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Volume of a pyramid is Thus: Area of the base is . Therefore, each side is .

What is the approximate volume of a square pyramid with one edge of the base measuring and a height equal to the diagonal of its base?

If one edge of the base is 2.7 inches, and the height of the pyramid is equal to the diagonal of the base, we can find the height using the edge. The height is going to be equal to . The area of the base is . Volume of a pyramid is equal to This leaves us with

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters. Since the base is a square, the area of the base is 3 x 3 = 9. Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Volume of a pyramid is Thus: Area of the base is . Therefore, each side is .

What is the approximate volume of a square pyramid with one edge of the base measuring and a height equal to the diagonal of its base?

If one edge of the base is 2.7 inches, and the height of the pyramid is equal to the diagonal of the base, we can find the height using the edge. The height is going to be equal to . The area of the base is . Volume of a pyramid is equal to This leaves us with

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters. Since the base is a square, the area of the base is 3 x 3 = 9. Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Volume of a pyramid is Thus: Area of the base is . Therefore, each side is .

What is the approximate volume of a square pyramid with one edge of the base measuring and a height equal to the diagonal of its base?

If one edge of the base is 2.7 inches, and the height of the pyramid is equal to the diagonal of the base, we can find the height using the edge. The height is going to be equal to . The area of the base is . Volume of a pyramid is equal to This leaves us with

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters. Since the base is a square, the area of the base is 3 x 3 = 9. Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Volume of a pyramid is Thus: Area of the base is . Therefore, each side is .

What is the approximate volume of a square pyramid with one edge of the base measuring and a height equal to the diagonal of its base?

If one edge of the base is 2.7 inches, and the height of the pyramid is equal to the diagonal of the base, we can find the height using the edge. The height is going to be equal to . The area of the base is . Volume of a pyramid is equal to This leaves us with

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters. Since the base is a square, the area of the base is 3 x 3 = 9. Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Volume of a pyramid is Thus: Area of the base is . Therefore, each side is .

What is the approximate volume of a square pyramid with one edge of the base measuring and a height equal to the diagonal of its base?

If one edge of the base is 2.7 inches, and the height of the pyramid is equal to the diagonal of the base, we can find the height using the edge. The height is going to be equal to . The area of the base is . Volume of a pyramid is equal to This leaves us with

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters. Since the base is a square, the area of the base is 3 x 3 = 9. Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Volume of a pyramid is Thus: Area of the base is . Therefore, each side is .

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

What is the approximate volume of a square pyramid with one edge of the base measuring $2.7\textup{inches}$ and a height equal to the diagonal of its base?

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

What is the approximate volume of a square pyramid with one edge of the base measuring $2.7\textup{inches}$ and a height equal to the diagonal of its base?

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

What is the approximate volume of a square pyramid with one edge of the base measuring $2.7\textup{inches}$ and a height equal to the diagonal of its base?

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

What is the approximate volume of a square pyramid with one edge of the base measuring $2.7\textup{inches}$ and a height equal to the diagonal of its base?

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

What is the approximate volume of a square pyramid with one edge of the base measuring $2.7\textup{inches}$ and a height equal to the diagonal of its base?

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

What is the approximate volume of a square pyramid with one edge of the base measuring $2.7\textup{inches}$ and a height equal to the diagonal of its base?

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .