32
AssignmentMultiple Select

Volume of Pyramids

Question 32 • (OC27) GEO-1206310-S2-Degele-VOL7006P

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.

Answer
A
The cabinets have the same base area.
B
The base area of the oblique prism is smaller than the base area of the right prism.
C
The cabinets may have the same base dimensions.
D
The cabinets may have different base dimensions.
E
The base area of the right prism is smaller than the base area of the oblique prism.

Explanation

For either prism, volume equals base area times perpendicular height. Each cabinet has volume 4,608 cubic inches and height 48 inches, so each base area is 4,608 ÷ 48 = 96 square inches. Thus, the base areas are the same. The bases could have the same dimensions or different dimensions while still having the same area; the 64-inch edge length does not change this calculation.

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