Question

STRUCTURE Write the ratio of the side lengths of the two cubes described in simplest form. a. The volumes of the two cubes are 270x cubic inches and 32x2 cubic inches. b. The surface areas of the two cubes are 6x4 square feet and 6(x + 1) square feet.

Answer 1

a)
`2.036x^-(1)/(3)`

b)
`(x^2)/(√(x+1) )`

Explanation:

For a cube, all the sides are equal. Let the length of each side be L

a) The volume of a cube (V) = L³

For the first cube:

V = 270x in³

270x = L³

L = ∛(270x) =
`6.463x^(1)/(3)`

For the second cube:

V = 32x² in³

32x² = L³

L = ∛(32x²) =
`3.175x^(2)/(3)`

Ratio of length =
`(6.463x^(1)/(3) )/(3.175x^(2)/(3) )=2.036x^-(1)/(3)`

b) The surface area of a cube (s) = 6L²

For the first cube:

s = 6x⁴ ft²

6x⁴ = L²

L = √6x⁴= 2.45x²

For the second cube:

s = 6(x + 1) ft²

6(x + 1) = L²

L = √6(x + 1)= 2.45√(x + 1)

Ratio of the length =
`(2.45x^2)/(2.45√( (x + 1))) =(x^2)/(√(x+1) )`