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SAT Math : How to find the volume of a pyramid

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Example Questions

Example Question #281 : Geometry

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

Possible Answers:

$1.5\ ft$

$2\ ft$

$4\ ft^{2}$

$2\ ft^{2}$

$4\ ft$

Correct answer:

$2\ ft$

Explanation:

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 $2\ ft$ .

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Example Question #1 : Pyramids

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.

Possible Answers:

Correct answer:

Explanation:

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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Example Question #52 : Solid Geometry

Find the volume of the pyramid shown below:

Screen shot 2015 10 27 at 3.33.57 pm

Possible Answers:

689

432

$\frac{17}{3}$

144

Correct answer:

144

Explanation:

The formula for the area of a pyramid is $\frac{lwh}{3}$ . In this case, the length is , the width is , and the height is .

$8\times6\times9=432$ and $439\div3=144$ .

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Example Question #4 : Pyramids

Pyramid question

Figure not drawn to scale

In the pyramid above, the base is a square. The distance between points C and D is 6 inches and the length of side b is 5 inches. What is the volume of this pyramid?

Possible Answers:

$12\ cm^3$

$25\ cm^3$

$24\ cm^3$

$10\ cm^3$

$30\ cm^3$

Correct answer:

$24\ cm^3$

Explanation:

Pyramid question notes1

To find the volume of a pyramid, you need to use the equation below:

$Volume=\frac{(area\, of\, the\, base)(height)}{3}$

To find the height (shown by the yellow line), we can draw a right triangle using the yellow line, blue line and side b (5 inches). Because the hypotenuse is 5 inches, using the common Pythagorean 3-4-5 triple. The blue line is 3 inches and the yellow line (height) is 4 inches. Also, to find side a, we can use the blue line (3 inches) and half of the red line (3 inches) and the Pythagorean Theorum.

$3^2+3^2=(side\, a)^2$

$9+9=(side\, a)^2$

$18=(side\, a)^2$

$\sqrt{18}\, in=side\, a$

Because the base is a square, the area of the base is equal to the square of side a:

$(side a)^2=18\: in^2$

Now we plug in these values to find the volume:

$Volume=\frac{(18)(4)}{3}$

$Volume=\frac{(72)}{3}$

$Volume=24\, in^3$

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Example Question #3 : Pyramids

Pyramid

Calculate the volume of the rectangular pyramid with height h=4in. , base width w=6in. , and base length l=6in.

Possible Answers:

72in.^3

32in.^3

60in.^3

48in.^3

36in.^3

Correct answer:

48in.^3

Explanation:

The volume of a rectangular pyramid with height , base width , and base length is given by

$V=\frac{1}{3}lwh$ .

For this pyramid, h=4in. , w=6in. , and l=6in. To calculate its volume, substitute the values for , , and into the formula:

$V=\frac{1}{3}(6)(6)(4)=\frac{144}{3}=48$

Therefore, the volume of the given rectangular pyramid is 48in.^3

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SAT Math : How to find the volume of a pyramid

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #281 : Geometry

Example Question #1 : Pyramids

Example Question #52 : Solid Geometry

Example Question #4 : Pyramids

Example Question #3 : Pyramids

All SAT Math Resources

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