Question

An employee at a factory is designing a new shipping container. Two views of the container are shown below.

Isometric view of container shows two rectangular prisms connected. The bigger prism has longest side w. Side view of container shows shortest side and width of bigger prism as 6 inches and 2 inches. The smaller prism has a side 2 inches. Base connecting both the prisms has a length of 8 inches. The slant height between the prisms has a length of 5 inches.

The shipping container must have a volume of 240 cubic inches.

Based on the information, what is
w
, the width of the container? Show work and explain your answer.

Type your answer in the box below.

Answer 1

Interpret the side view as two rectangular prisms sitting end-to-end along a common base. The vertical difference between their tops is 6 − 2 = 4 in, and the slanted top between them is length 5 in, so by Pythagoras the horizontal distance between their top edges is sqrt(5^2 − 4^2) = 3 in. The base total 8 in is therefore split as 3 in (big prism) + 5 in (small prism).

Let w be the common width (the longest side of the bigger prism). Then
- volume of the bigger prism = height × base-length × width = 6 × 3 × w = 18w,
- volume of the smaller prism = 2 × 5 × w = 10w.

Total volume = 18w + 10w = 28w. Set equal to 240:
28w = 240 ⇒ w = 240/28 = 60/7.

Answer: w = 60/7 inches (≈ 8.571 in).