Geometry question

Question

Given the total surface area of a cube is 294 cm2, determine the volume of the cube.

Answer 1

Work your way backwards, and look at the formulas you'll need. The volume of a cube is the length of a side of the cube, cubed (x*x*x, or x^3). Recall also how you get the surface area of a cube in the first place. A cube is six squares made up of that same length (x). Area of a square is x^2, and then you just multiply it by 6 to get all six squares, and that totals up to 294. So 6*x^2 = 294.

Great, that's all the information we need. Start by solving for x, and then plug that x into the volume formula.

For reference, I got x = 7cm and the volume therefore as 343cm^3.

(Don't forget to add the units you're working in to your answer!)

Answer 2

Surface area of a cube = 6e^2, where e is the length of an edge, so:

6e^2 = 294 cm^2

e^2 = 49 cm^2

e = 7 cm

Volume of a cube = e^3

so volume = 7^3 cm^3 = 343 cm^3