Question

What is the volume of the cube if it's surface area is $2400{\mathrm{cm}}^2$?

Answer 1

Find the volume of the cube
The surface area of a cube is $2400{\mathrm{cm}}^2$

'Also formula of the surface area of a cube is $6a^2$.

Where $a$ is the edge of cube.

Equate the given surface area to the formula mentioned above to determine the length of the edge:
$$\begin{gathered} \mathrm{Surface}\mathrm{area}=2400 \\ \begin{array}{rcl}& \Rightarrow & 6a^2=2400\\ & \Rightarrow & a^2=\frac{2400}{6}\\ & \Rightarrow & a^2=400\\ & \Rightarrow & a=\sqrt{400}\\ & \Rightarrow & a=20\end{array} \end{gathered}$$
so, the side of the cube is $20\mathrm{cm}$
The volume of the cube is $a^3$
Calculate the volume $V$ of the cube as follow:

$\begin{array}{rcl}V& =& {\mathrm{a}}^3\\ & \Rightarrow & V=20\times 20\times 20\\ & \Rightarrow & V=800{\mathrm{cm}}^3\end{array}$

Hence the volume of the cube is $800{\mathrm{cm}}^3.$