Please help. Thank you!

Question

The volume of a cube with a surface area of 384 in^2 is ____ in^3.

Answer 1

Hi there!

For this question, the two key equations that you need are the formulas for the surface area of a cube and volume of a cube

Surface Area: S = 6a², where a is the length of a side of the cube

Volume: V = a³

We are given that S = 384in². Therefore, we can plug this into our surface area equation to solve for a, and then plug that value of a into our volume equation to ultimately find V.

384 = 6a² Divide both sides of the equation by 6

64 = a² Take the square root of both sides

a = 8

Now that we know that the length of a side of the cube is 8in, we can plug this into our equation for volume.

V = (8)³

V = 512

Thus, our final answer is that the volume of this cube is 512in³.

I hope that this explanation is helpful!