Volume of a Rectangular Solid - Pre-Algebra

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Question

A rectangular box has a length of 2 meters, a width of 0.5 meters, and a height of 3.2 meters. How many cubes with a volume of one cubic centimeter could fit into this rectangular box?

Answer

In order to figure out how many cubic centimeters can fit into the box, we need to figure out the volume of the box in terms of cubic centimeters. However, the measurements of the box are given in meters. Therefore, we need to convert these measurements to centimeters and then determine the volume of the box.

There are 100 centimeters in one meter. This means that in order to convert from meters to centimeters, we must multiply by 100.

The length of the box is 2 meters, which is equal to 2 x 100, or 200, centimeters.

The width of the box is 0.5(100) = 50 centimeters.

The height of the box is 3.2(100) = 320 centimeters.

Now that all of our measurements are in centimeters, we can calculate the volume of the box in cubic centimeters. Remember that the volume of a rectangular box (or prism) is equal to the product of the length, width, and height.

V = length x width x height

V = (200 cm)(50 cm)(320 cm) = 3,200,000 cm3

To rewrite this in scientific notation, we must move the decimal six places to the left.

V = 3.2 x 106 cm3

The answer is 3.2 x 106.

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Question

If a cube is inches tall, what is its volume?

Answer

To find the volume of a cube, we multiply length by width by height, which can be represented with the forumla $v=l\cdot w\cdot h$ . Since a cube has equal sides, we can use for all three values.

$8\cdot 8\cdot 8=512: in ^{3}$

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Question

What is the volume of a cube with a side length equal to inches?

Answer

The volume of a a cube (or rectangular prism) can be solved using the following equation:

$V=l\times\ w\times\ h$

$V=7in\times 7in\times 7in=343in^3$

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Question

Find the volume of a rectangular box if the length, width, and height are $\textup{6, 15, and 11,}$ respectively.

Answer

Write the formula to find the volume of a rectangular prism.

$V= \textup{Length} \times \textup{Width } \times \textup{Height}$

Substitute the dimensions.

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Question

A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its volume in cubic feet.

Answer

Divide each dimension in inches by 12 to convert from inches to feet:

$L = 24 \div 12 = 2$ feet

$W = 18 \div 12 = 1 \frac{1}{2} = \frac{3}{2}$ feet

$H = 15 \div 12 = 1 \frac{1}{4} = \frac{5}{4}$ feet

Multiply the three to get the volume:

$V = LWH = 2 \cdot \frac{3}{2} \cdot \frac{5}{4} = \frac{15}{4} = 3 \frac{3}{4}$ cubic feet

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Question

The volume of a cube is . What is the length of an edge of the cube?

Answer

Let be the length of an edge of the cube. The volume of a cube can be determined by the equation:

$\sqrt[3]{x^3}=\sqrt[3]{64}$

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Question

Trayvon ordered a new calculator online for his Pre-Algebra class. When it arrived in the mail, he noticed something interesting about the rectangular box it was shipped in. The width of the box was twice the height, and the length of the box was three times the width. If the box was four inches tall, what was the volume of the box?

Answer

If the box is 4 inches tall, then its height is 4in. Since the width is twice the height, the width must be 8 inches. Since the length is three times the width, the length must be 24 inches. Since a rectangular box is just a rectangular solid, the formula for the volume of a rectangular solid will give us the volume of the Trayvon's box.

, where is length, is width, and is height. Therefore,

Since the unit of each of our dimensions was inches, our volume will be in cubic inches. Thus our answer is $768in.^{3}$

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Question

An aquarium is shaped like a perfect cube; the perimeter of each glass face is meters. If it is filled to the recommended capacity, then, to the nearest hundred cubic liters, how much water will it contain?

Note: $1\textup{ cubic meter}= 1\textup{,}000\textup{ cubic liters}$

Answer

A perfect cube has square faces; if a face has perimeter meters, then each side of each face measures one fourth of this, or meters. The volume of the tank is the cube of this, or

$2.1^{3} = 9.261$ cubic meters.

Its capacity in liters is $9.261 \times 1,000 = 9,261$ liters.

of this is

$9,261 \times 0.9 = 8,335$ liters.

This rounds to $8\textup,300$ liters, the correct response.

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Question

A given rectangular prism has a length of , a width of , and a height of . What is the volume of the prism?

Answer

The volume of a given prism , where is the base area and is the height. For a rectangular prism, the base area $B=l \times w$ , or length times width. Therefore:

$V=(l\times w)h$

Substituting in our known values:

$V=(9:cm\times 5:cm)7:cm$

$V=45:cm^{2}\times 7:cm$

$V=315:cm^{3}$

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Question

A given rectangular prism has a length of , a width of , and a height of . What is the volume of the prism?

Answer

The volume of a rectangular prism is the product of its base area and its height : . Since we can determine the base area of the rectangular prism from its length and width, we can rewrite the equation and solve:

$V=12 \times48$

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Question

A given rectangular prism has a length of , a width of , and a height of , what is its volume?

Answer

The volume of a rectangular prism is the product of its base area and its height : . Since we can determine the base area of the rectangular prism from its length and width, we can rewrite the equation and solve:

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Question

The length, width, and height of box is respectively. What is the volume of the rectangular box?

Answer

Write the formula to find the volume of a rectangular solid.

$V=\textup{ Length} \times \textup{Width} \times\textup{ Height}$

Substitute the dimensions.

$2\times5\times9 = 90$

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Question

Find the volume of a rectangular solid if the base area is and the height is .

Answer

Write the formula to find the volume of the rectangular solid.

$V= LWH = A_{base}H$

The area of the base is length times width, and is already given. Multiply the area of the base with the height to obtain the volume.

$V=A_{base}H = 4(6)=24$

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Question

Find the volume of the rectangular solid if the base has an area of and the height is .

Answer

Write the formula for the volume of a rectangular solid.

$V=\textup{LWH}$

The base area is:

$\textup{B}_\textup{Area} = \textup{LW} = 4$

Substitute the area and the height.

$V=\textup{(LW)H} = 4(5)=20$

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Question

A matchbox has a length of 10 inches, width of 2 inches and height of 1 inch. What is the volume of the matchbox?

Answer

To find the volume of a rectangular solid you must multiply the length, width, and height together.

Volume is in units cubed.

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Question

Find the volume of a rectangular solid with a length of 4, a width of 1, and a height of 10.

Answer

Write the formula to find the volume of the rectangular solid.

$V=\textup{Length } \times\textup{ Width }\times\textup{ Height}$

Substitute the known dimensions.

$V=4 \times 1\times 10$

Multiply the numbers.

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Question

Alfred has a fish tank that looks like this:

Alfred needs to fill the tank with water. To do that, he needs to know the volume of the tank. Find the volume of the tank if the height is 12 inches, the length is three times the height, and the width is the same as the height.

Answer

The fish tankbis considered a rectangular prism. The formula to find the volume of a rectangular prism is

$V = l \cdot w \cdot h$

where l is the length, w is the width, and h is the height. We know the height is 12 inches. The length is three times the height, so the length is 36 inches. The width is the same as the height, sonthe width is 12 inches. Now, we can substitute. We get

$V = 36 \text{ inches} \cdot 12 \text{ inches} \cdot 12 \text{ inches}$

$V = 5184 \text{ inches}^3$

Therefore, the volume of the fish tank is $5184 \text{ inches}^3$ .

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Question

Find the volume of a rectangular box with the following dimensions:

Length: 4 feet. Width: 12 feet. Height: 3 feet.

Answer

Find the volume of a rectangular box with the following dimensions:

Length: 4 feet. Width: 12 feet. Height: 3 feet.

To find volume of a rectangular box, we just need to use the following:

So our answer is:

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Question

A rectangular box has a length of 2 meters, a width of 0.5 meters, and a height of 3.2 meters. How many cubes with a volume of one cubic centimeter could fit into this rectangular box?

Answer

In order to figure out how many cubic centimeters can fit into the box, we need to figure out the volume of the box in terms of cubic centimeters. However, the measurements of the box are given in meters. Therefore, we need to convert these measurements to centimeters and then determine the volume of the box.

There are 100 centimeters in one meter. This means that in order to convert from meters to centimeters, we must multiply by 100.

The length of the box is 2 meters, which is equal to 2 x 100, or 200, centimeters.

The width of the box is 0.5(100) = 50 centimeters.

The height of the box is 3.2(100) = 320 centimeters.

Now that all of our measurements are in centimeters, we can calculate the volume of the box in cubic centimeters. Remember that the volume of a rectangular box (or prism) is equal to the product of the length, width, and height.

V = length x width x height

V = (200 cm)(50 cm)(320 cm) = 3,200,000 cm3

To rewrite this in scientific notation, we must move the decimal six places to the left.

V = 3.2 x 106 cm3

The answer is 3.2 x 106.

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Question

If a cube is inches tall, what is its volume?

Answer

To find the volume of a cube, we multiply length by width by height, which can be represented with the forumla $v=l\cdot w\cdot h$ . Since a cube has equal sides, we can use for all three values.

$8\cdot 8\cdot 8=512: in ^{3}$

Compare your answer with the correct one above

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