To find the volume of a cube, we multiply length by width by height, which can be represented with the forumla $\displaystyle v=l\cdot w\cdot h$.  Since a cube has equal sides, we can use $\displaystyle 8$ for all three values.

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

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

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

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

Let $\displaystyle s$ 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 $\displaystyle \frac{150}{6} = 25$ square inches. Therefore, $\displaystyle s^{2} = 25$, and $\displaystyle s = 5$.

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

First, the value of x must be solved for:

$\displaystyle x=5(4+3^{2})-3$

$\displaystyle x=5(4+9)-3$

$\displaystyle x=5(13)-3$

$\displaystyle x=62$

Given the edge of the cube is $\displaystyle \sqrt[3]{x}$, plugging in the value of x results in $\displaystyle \sqrt[3]{62}$. Thus, the area would be equal to this value cubed, which would result in 62. 

Thus, 62 is the correct answer. 

Since a diagonal of a square face of the cube is$\displaystyle N$, each side of each square has length $\displaystyle \frac{N}{\sqrt{2}}=\frac{N\sqrt{2}}{2}$.

Cube this to get the volume of the cube:

$\displaystyle \left (\frac{N\sqrt{2}}{2} \right )^{3}$

$\displaystyle = \frac{N^{3}\left ( \sqrt{2} \right )^{3} }{2^{3} }$

$\displaystyle = \frac{N^{3} \cdot 2 \sqrt{2} }{8}$

$\displaystyle = \frac{N^{3} \sqrt{2} }{4}$

Let $\displaystyle s$ be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem, 

$\displaystyle s^{2}+s^{2}+s^{2}=1.5^{2}$

$\displaystyle 3s^{2}=2.25$

$\displaystyle s^{2} = 0.75 = \frac{3}{4}$

$\displaystyle s = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{\sqrt{4}}} = \frac{\sqrt{3}}{2}$ meters.

Cube this sidelength to get the volume:

$\displaystyle s ^{3 } =\left ( \frac{\sqrt{3}}{2} \right )^{3 }= \frac{\left (\sqrt{3}\right )^{3 }}{2^{3 } } = \frac{ 3\sqrt{3} }{8 }$ cubic meters.

To convert this to liters, multiply by 1,000:

$\displaystyle \frac{ 3\sqrt{3} }{8 } \cdot 1,000 = \frac{ 3\sqrt{3} }{8 } \cdot \frac{1,000}{1} = \frac{ 3\sqrt{3} }{1 } \cdot \frac{125}{1}= 375\sqrt{3}$ liters.

This is not among the given responses.

Let $\displaystyle s$ 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 $\displaystyle \frac{240}{6} = 40$ square inches. Therefore, $\displaystyle s^{2} = 40$, and $\displaystyle s = \sqrt{40} = 2\sqrt{10}$.

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

A perfect cube has square faces; if a face has perimeter $\displaystyle 8.4$ meters, then each side of each face measures one fourth of this, or $\displaystyle 2.1$ meters. The volume of the tank is the cube of this, or

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

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

$\displaystyle 90\%$ of this is 

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

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

Your friend gives you a puzzle cube for your birthday. If the length of one edge is 5cm, what is the volume of the cube?

To find the volume of a cube, use the following formula:

$\displaystyle V_{cube}=s^3$

Where s is the side length.

Plug in what we know to get our answer:

$\displaystyle V=(5cm)^3=125cm^3$

A cube has a side length of $\displaystyle 9 mm$, what is the volume of the cube?

To find the volume of a cube, use the following formula:

$\displaystyle V_{cube}=s^3$

Plug in our known side length and solve

$\displaystyle V_{cube}=(9mm)^3=729mm^3$

Making our answer:

$\displaystyle 729mm^3$