Video Transcript
What is the surface area of a cube
if its volume is eight cubic centimeters?
We are given the volume of a cube
and asked to find its surface area. To answer this question, we need to
recall the formula for the volume of a cube, which is length cubed, and the formula
for the surface area of a cube, which is six times the length squared. We recall that all dimensions of a
cube, including its height, width, and depth, are equal. Therefore, we can label all
dimensions as 𝑙 centimeters.
Knowing that the volume is eight,
we can set up the equation eight equals 𝑙 cubed. Then, we solve for 𝑙 by taking the
cube root of eight. So we get 𝑙 is equal to two. Now that we have the side length of
the cube, we can substitute this value for 𝑙 in the surface area equation. Using proper order of operations,
we first square two then multiply by six. Hence, the surface area of a cube
with a volume of eight cubic centimeters is 24 square centimeters.
