Video Transcript
Find the side length of a cube
given that its volume is 27 over eight cubic centimeters.
We begin by recalling that a cube
of side length 𝑙 centimeters will have a volume of 𝑙 cubed cubic centimeters. This means that in this question,
𝑙 cubed is equal to 27 over eight or twenty-seven eighths. We note that both 27 and eight are
perfect cubes, since three cubed is equal to 27 and two cubed is equal to eight. We can therefore rewrite our
equation as 𝑙 cubed is equal to three cubed over two cubed. In order to solve this, we take the
cube root of both sides. Recalling that if 𝑎 and 𝑏 are
integers and 𝑏 is nonzero, then the cube root of 𝑎 cubed over 𝑏 cubed is equal to
𝑎 over 𝑏. Then, the right-hand side of our
equation simplifies to three over two. And we can therefore conclude that
the side length of a cube with a volume of 27 over eight cubic centimeters is three
over two centimeters. It is also worth noting we could
write this in decimal form of 1.5 centimeters.
