7th Grade Math - Finding Volume of a Rectangular Prism

Box

The above diagram shows a rectangular solid. The shaded side is a square. In terms of , give the volume of the box.

$15x^{2}$

$4x^{2} + 30 x$

Explanation

A square has four sides of equal length, as seen in the diagram below.

Box

The volume of the solid is equal to the product of its length, width, and height, as follows:

$V = 15 \cdot 15 \cdot x =225 x$ .

Calculate the volume of the provided figure.

$240\textup{ in}^3$

$241\textup{ in}^3$

$242\textup{ in}^3$

$243\textup{ in}^3$

$244\textup{ in}^3$

Explanation

In order to solve this problem, we need to recall the volume formula for a rectangular prism:

$V=l\times w\times h$

Now that we have the correct formula, we can substitute in our known values and solve:

$V=10\times4\times6$

$V=240\textup{ in}^3$

Calculate the volume of the provided figure.

$144\textup{ in}^3$

$145\textup{ in}^3$

$143\textup{ in}^3$

$142\textup{ in}^3$

$141\textup{ in}^3$

Explanation

In order to solve this problem, we need to recall the volume formula for a rectangular prism:

$V=l\times w\times h$

Now that we have the correct formula, we can substitute in our known values and solve:

$V=9\times4\times4$

$V=144\textup{ in}^3$

A rectangular prism has the following dimensions:

Length:

Width:

Height:

Find the volume.

Explanation

Given that the dimensions are: , , and and that the volume of a rectangular prism can be given by the equation:

$v=l \cdot w \cdot h$ , where is length, is width, and is height, the volume can be simply solved for by substituting in the values.

This final value can be approximated to .

Solve for the volume of a prism that is 4m by 3m by 8m.

Explanation

The volume of the rectangle

so we plug in our values and obtain

The dimensions of Treasure Chest A are 39” x 18”. The dimensions of Treasure Chest B are 16” x 45”. Both are 11” high. Which of the following statements is correct?

Treasure Chest A and B can hold the same amount of treasure.

Treasure Chest A can hold more treasure.

Treasure Chest B can hold more treasure.

Treasure Chest A has the same surface area as Treasure Chest B.

There is insufficient data to make a comparison between Treasure Chest A and Treasure Chest B.

Explanation

The volume of B is 7920 in3. The volume of A is 7722 in3. Treasure Chest B can hold more treasure.

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

Explanation

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

Find the volume of a rectangular prism via the following:

Where l, w, and h are the length width and height, respectively.

We know our length and width, and we are told that our height is triple the length, so...

Now that we have all our measurements, plug them in and solve:

Calculate the volume of the provided figure.

$180\textup{ in}^3$

$181\textup{ in}^3$

$182\textup{ in}^3$

$183\textup{ in}^3$

$184\textup{ in}^3$

Explanation

In order to solve this problem, we need to recall the volume formula for a rectangular prism:

$V=l\times w\times h$

Now that we have the correct formula, we can substitute in our known values and solve:

$V=12\times5\times3$

$V=180\textup{ in}^3$

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

$8\textup,300\textup{ L}$

$9\textup,300\textup{ L}$

$4\textup,400\textup{ L}$

$4\textup,000\textup{ L}$

Insufficient information is given to answer the question.

Explanation

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