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:

\(\displaystyle 729mm^3\)