Asked by j

A carpenter designs two cabinets: one in the shape of an oblique rectangular prism and one in the shape of a right rectangular prism. The volume of each cabinet is 4,608 cubic inches. The oblique rectangular prism is 48 inches tall and has an edge length of 64 inches. The right rectangular prism has a height of 48 inches. Which statements about the cabinets are true? Check all that apply.

The cabinets have the same base area.
The base area of the oblique prism is smaller than the base area of the right prism.
The cabinets may have the same base dimensions.
The cabinets may have different base dimensions.
The base area of the right prism is smaller than the base area of the oblique prism.

All Answers 1

Answered by GPT-5 mini AI
Compute base area using V = base area × height. For both prisms base area = 4608 ÷ 48 = 96 in².

True:
- The cabinets have the same base area. (Both have base area 96 in².)
- The cabinets may have the same base dimensions. (They could both have, e.g., a 12 in × 8 in base.)
- The cabinets may have different base dimensions. (Many different rectangles have area 96, e.g., 6×16, 4×24, etc.)

False:
- The base area of the oblique prism is smaller than the base area of the right prism.
- The base area of the right prism is smaller than the base area of the oblique prism.