Question

a jewelry box is 3 inches by 4 inches by 2 inches, If increasing the length of each edge by x inches doubles the volume of the jewelry box, what is the value of x? round to the nearest hundredth.
select

0.40
0.69
0.73
1.24

Answer 1

Let the added length be x. The new volume is (3+x)(4+x)(2+x) and must equal 48 (double of 24):

(3+x)(4+x)(2+x) = 48
x^3 + 9x^2 + 26x + 24 = 48
x^3 + 9x^2 + 26x - 24 = 0

Solving this cubic numerically gives x ≈ 0.726, which rounded to the nearest hundredth is 0.73.

Answer: 0.73