Question

The volume of a cube of ice for an ice sculpture is $64,000$ cubic inches.

What is the surface area of the cube of ice?

Answer 1

Step 1: Find the edge length of a cube of rice.

Given: Volume of a cube of ice $=64,000$ cubic inches.

We know that

volume of the cube $={(\mathrm{side})}^3$

Let $s$ be the edge length of cube of ice.

Now, according to the question,

$$\begin{gathered} s^3=64000 \\ \Rightarrow s=\sqrt[3]{64000} \\ \Rightarrow s=\sqrt[3]{{\left(40\right)}^3} \end{gathered}$$

$\Rightarrow s=40$ ( cancel cube with cube root )

Hence, the edge length of the cube of ice is $40$ inches.

Step 2: Find the surface area of a cube of rice.

We know that

Surface area of a cube $=6s^2$

Now,

Surface area of a cube of rice $=6s^2$

$$\begin{gathered} =6{\left(40\right)}^2 \\ =6\times 40\times 40 \end{gathered}$$

$=9600$ square inches.

Hence, the surface area of the cube of ice is $9600$ square inches.