Pre-Algebra - Volume of a Rectangular Solid

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

Explanation

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

Volume is in units cubed.

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

Explanation

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

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

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

Explanation

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.

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

$3 \frac{3}{4} \textrm{ ft}^{3}$

$4 \frac{3}{4} \textrm{ ft}^{3}$

$4 \frac{1}{4} \textrm{ ft}^{3}$

$4 \frac{1}{2} \textrm{ ft}^{3}$

Explanation

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

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

Not enough information provided.

Explanation

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.

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

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

$343: in^{3}$

$49: in^{3}$

$21: in^{3}$

$53: in^{3}$

Explanation

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

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

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

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

Explanation

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.

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

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

Explanation

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.

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

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

$1050cm^{3}$

$1050cm^{2}$

$32cm^{3}$

$85cm^{3}$

$525cm^{3}$

Explanation

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: