Question

a hollow cubical pencil holder has a volume of 512 cm³. what is the outer surface area of the five sides of the holder?

Explanation:

Step1: Find the side - length of the cube

The volume formula for a cube is $V = s^{3}$, where $V$ is the volume and $s$ is the side - length. Given $V = 512\ cm^{3}$, we solve for $s$:
\[s=\sqrt[3]{V}=\sqrt[3]{512}=8\ cm\]

Step2: Calculate the outer surface area of five sides

The surface area formula for one face of a cube is $A_{face}=s^{2}$. The outer surface area of five sides of the cube is $A = 5s^{2}$.
Substitute $s = 8\ cm$ into the formula:
\[A = 5\times8^{2}=5\times64 = 320\ cm^{2}\]

Answer:

$320\ cm^{2}$