A box shaped like a rectangular prism has a height of 17 in and a volume of 2,720 in3. The length is 4 inches greater than twice the width. What is the width of the box?
Solution:
Given, volume of rectangular prism = 2,720 in3
Height of prism = 17 in
Let, length be L and width be W
Length = 4 + 2 width
L = 4 + 2W
We have to find the width of the box.
Volume = length × width × height
2720 = L × W × 17
2720 = (4 + 2W) × W × 17
(4 + 2W) × W = 2720 / 17
(4 + 2W) × W = 160
4W + 2W2 = 160
2W2 + 4W - 160 = 0
Dividing by 2
W2 + 2W - 80 = 0
On solving,
W2 + 10W - 8W - 80 = 0
W(W + 10) - 8(W + 10) = 0
(W - 8)(W + 10) = 0
W - 8 = 0
W = 8
W + 10 = 0
W = -10
The value cant be negative
Therefore, the width of the box is 8 in.
A box shaped like a rectangular prism has a height of 17 in and a volume of 2,720 in3. The length is 4 inches greater than twice the width. What is the width of the box?
Summary:
A box shaped like a rectangular prism has a height of 17 in and a volume of 2,720 in3. The length is 4 inches greater than twice the width. The width of the box is 8 in.
Math worksheets and
visual curriculum
visual curriculum