Answer to Question #276771 in Geometry for Leyahhhh

Question

5) A fruit crate has square ends and is twice as long as it is wide.

(a) Find the volume of the crate if its width is 20 inches.

(b) Find a formula for the volume V of the crate in terms of its width x.

Answer 1

a) The width is 20 inches and is one of the sides of a square end.

So the height is 20 inches. The crate is twice as long as it is wide so the length is 40 inches

Volume equals width times length times height

So the volume of the crate is $20\times 40\times 20 = 16000$ cubic inches

b) Width = x

length =2x

height = x

volume, $V= x \times 2x \times x=2x^3$