Solve Problems Involving Area, Volume and Surface Area of Two- and Three-Dimensional Objects: CCSS.Math.Content.7.G.B.6 - Common Core: 7th Grade Math

Card 0 of 20

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

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:

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

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

Compare your answer with the correct one above

Question

Give the volume of a cube with surface area 240 square inches.

Answer

Let be the length of one edge of the cube. Since its surface area is 240 square inches, one face has one-sixth of this area, or $\frac{240}{6} = 40$ square inches. Therefore, $s^{2} = 40$ , and $s = \sqrt{40} = 2\sqrt{10}$ .

The volume is the cube of this, or $V= \left ( 2\sqrt{10} \right )^{3}= 2^{3} \cdot \left ( \sqrt{10} \right )^{3}= 8 \cdot 10 \sqrt{10}= 80 \sqrt{10}$ cubic inches.

Compare your answer with the correct one above

Question

Give the volume of a cube with surface area 150 square inches.

Answer

Let be the length of one edge of the cube. Since its surface area is 150 square inches, one face has one-sixth of this area, or $\frac{150}{6} = 25$ square inches. Therefore, $s^{2} = 25$ , and .

The volume is the cube of this, or $V= 5^{3}=125$ cubic inches.

Compare your answer with the correct one above

Question

Calculate the volume of the provided figure.

Answer

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

$V=l\times w\times h$

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

$V=7\times7\times7$

$V=343\textup{ in}^3$

Compare your answer with the correct one above

Question

Calculate the volume of the provided figure.

Answer

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

$V=l\times w\times h$

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

$V=6\times6\times6$

$V=216\textup{ in}^3$

Compare your answer with the correct one above

Question

Calculate the volume of the provided figure.

Answer

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

$V=l\times w\times h$

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

$V=11\times11\times11$

$V=1\textup,331\textup{ in}^3$

Compare your answer with the correct one above

Question

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?

Answer

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

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

Question

A rectangular prism has the following dimensions:

Length:

Width:

Height:

Find the volume.

Answer

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 .

Compare your answer with the correct one above

Question

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

Answer

The volume of the rectangle

so we plug in our values and obtain

.

Compare your answer with the correct one above

Question

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

Answer

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

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

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

Compare your answer with the correct one above

Question

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.

Answer

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:

Compare your answer with the correct one above

Question

Calculate the volume of the provided figure.

Answer

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:

$V=10\times4\times6$

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

Compare your answer with the correct one above

Question

Calculate the volume of the provided figure.

Answer

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:

$V=9\times4\times4$

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

Compare your answer with the correct one above

Question

Calculate the volume of the provided figure.

Answer

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:

$V=12\times5\times3$

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

Compare your answer with the correct one above

Question

Calculate the area of the provided figure.

Answer

In order to solve this problem, we need to recall the area formula for a circle:

$A=r^2\pi$

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

$A=12^2\pi$

$A=144\pi\textup{ in}^2$

Compare your answer with the correct one above

Question

Calculate the area of the provided figure.

Answer

In order to solve this problem, we need to recall the area formula for a circle:

$A=r^2\pi$

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

$A=19^2\pi$

$A=361\pi\textup{ in}^2$

Compare your answer with the correct one above

Question

Calculate the area of the provided figure.

Answer

In order to solve this problem, we need to recall the area formula for a rectangle:

$A=l\times w$

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

$A=12\times10$

$A=120\textup{ in}^2$

Compare your answer with the correct one above

Question

Calculate the area of the provided figure.

Answer

In order to solve this problem, we need to recall the area formula for a rectangle:

$A=l\times w$

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

$A=11\times4$

$A=44\textup{ in}^2$

Compare your answer with the correct one above

Tap the card to reveal the answer