Question

Solve.

1) A rectangular box is 6 in. high. The length is 2 in. more than the width. If the
volume of the box is 480 in³, find the length and width of the box.
W + 2
W
6 in.

Answer 1

length = 10 in.

width = 8 in.

Explanation:

volume of cuboid = length(l) * width(w) * height(h)

l = w + 2

(w + 2) * w * 6 = 480

(w + 2) * w = 480/6 = 80 in²

w² + 2w = 80

w² + 2w - 80 = 0

solve for w (AC method):

w² + 10w - 8w - 80 = 0

w(w + 10) - 8 (w + 10) = 0

(w-8)(w+10) = 0

w = 8 or w = -10

As length cannot be negative, w = 8 in.

substitute w with 8:

l = 8 + 2 = 10 in.

10 * 8 * 6 = 480 in³