Math - Cubes | Practice Hub

A cube has a side length of meters. What is the volume of the cube?

$8\ \textup{m}^{3}$

$6\ \textup{m}^{3}$

$4\ \textup{m}^{3}$

$2\ \textup{m}^{3}$

$16\ \textup{m}^{3}$

Explanation

The formula for the volume of a cube is:

$Volume = (side)^{3}$

Since the length of one side is meters, the volume of the cube is:

$2^{3 } = 8$ meters cubed.

A cube has a side length of meters. What is the volume of the cube?

$8\ \textup{m}^{3}$

$6\ \textup{m}^{3}$

$4\ \textup{m}^{3}$

$2\ \textup{m}^{3}$

$16\ \textup{m}^{3}$

Explanation

The formula for the volume of a cube is:

$Volume = (side)^{3}$

Since the length of one side is meters, the volume of the cube is:

$2^{3 } = 8$ meters cubed.

If the surface area of a cube equals 96, what is the length of one side of the cube?

Explanation

The surface area of a cube = 6a2 where a is the length of the side of each edge of the cube. Put another way, since all sides of a cube are equal, a is just the lenght of one side of a cube.

We have 96 = 6a2 → a2 = 16, so that's the area of one face of the cube.

Solving we get √16, so a = 4

Find the length of an edge of the following cube:

Length_of_edge

The volume of the cube is $27\ m^3$ .

$3\ m$

$6\ m$

$9\ m$

$12\ m$

$15\ m$

Explanation

The formula for the volume of a cube is

where is the length of the edge of a cube.

Plugging in our values, we get:

$27\ m^3 = (e)^3$

$e = 3\ m$

If the surface area of a cube equals 96, what is the length of one side of the cube?

Explanation

The surface area of a cube = 6a2 where a is the length of the side of each edge of the cube. Put another way, since all sides of a cube are equal, a is just the lenght of one side of a cube.

We have 96 = 6a2 → a2 = 16, so that's the area of one face of the cube.

Solving we get √16, so a = 4

Find the length of an edge of the following cube:

Length_of_edge

The volume of the cube is $27\ m^3$ .

$3\ m$

$6\ m$

$9\ m$

$12\ m$

$15\ m$

Explanation

The formula for the volume of a cube is

where is the length of the edge of a cube.

Plugging in our values, we get:

$27\ m^3 = (e)^3$

$e = 3\ m$

Find the length of the diagonal of the following cube:

Length_of_diagonal

$4\sqrt{2}\ m$

$4\sqrt{3}\ m$

$4\ m$

$2\ m$

$8\ m$

Explanation

To find the length of the diagonal, use the formula for a triangle:

$a-a-a\sqrt{2}$

$4\ m-4\ m-4\sqrt{2}\ m$

The length of the diagonal is $4\sqrt{2}\ m$ .

$\textup{What is the surface area, in terms of }p,\textup{of a cube with sides of length }p\textup{ ?}$

$6p^{2}$

$p^{2}$

$4p^{2}$

$p^{3}$

Explanation

$\textup{Each of the six identical faces of the cube is a square with sides }p.$

$\textup{Each face: }A=p^{2}: : : : : \textup{Surface area}=6p^{2}$

Our backyard pool holds 10,000 gallons. Its average depth is 4 feet deep and it is 10 feet long. If there are 7.48 gallons in a cubic foot, how wide is the pool?

33 ft

30 ft

7.48 ft

100 ft

133 ft

Explanation

There are 7.48 gallons in cubic foot. Set up a ratio:

1 ft3 / 7.48 gallons = x cubic feet / 10,000 gallons

Pool Volume = 10,000 gallons = 10,000 gallons * (1 ft3/ 7.48 gallons) = 1336.9 ft3

Pool Volume = 4ft x 10 ft x WIDTH = 1336.9 cubic feet

Solve for WIDTH:

4 ft x 10 ft x WIDTH = 1336.9 cubic feet

WIDTH = 1336.9 / (4 x 10) = 33.4 ft

Find the length of the diagonal of the following cube:

Length_of_diagonal

$4\sqrt{2}\ m$

$4\sqrt{3}\ m$

$4\ m$

$2\ m$

$8\ m$

Explanation

To find the length of the diagonal, use the formula for a triangle:

$a-a-a\sqrt{2}$

$4\ m-4\ m-4\sqrt{2}\ m$

The length of the diagonal is $4\sqrt{2}\ m$ .

Cubes

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