Question

A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of

the new rectangular prism is 450 cubic inches. The equation 2y3+8x2-450 can be used to find x. What was the side
length of the original cube? Use a graphing calculator and a system of equations to find the answer.
O 4 inches
O5 inches
O 9 inches
O 10 inches

Answer 1

Explanation:

new dimensions of prism: x by (x+4) by (2x).

volume = x(x+4)(2x) = 2x³ + 8x²

2x³ + 8x² = 450

2x³ + 8x² - 450 = 0

x³ + 4x² - 225 = 0

x = 5 in

Answer 2

9514 1404 393

Answer:

(b) 5 inches

Explanation:

A graphing calculator makes short work of the problem. No system of equations is needed.

The volume of the new prism is ...

V = LWH

450 = x(x+4)(2x)

x(2x)(x+4) -450 = 0 . . . . . equation for graphing

The only real solution is x = 5.

The side length of the original cube was 5 inches.