Question

Test #2- Solids

Howard, Thomas
Jordan wash to prove the formula for the volume of the pyramid below by inserting the pyramid into a rectangular prism
Into which rectangular prism should Jordan insert the pyramid?
O
6n
6n
10.5 in
9h
105 in
10.5 in
oh
10.5 m
10.5 in
4
ous
on

Answer 1

Jordan should use option B: 6 in x 9 in x 6 in prism. Its volume matches the pyramid's, proving the formula.

The answer is the rectangular prism with the dimensions 6 inches by 6 inches by 9 inches. Here's why:

1. Volume formula: The volume of a pyramid is one-third the area of the base times the height. In this case, the area of the base is 6 inches x 6 inches = 36 square inches, and the height is 10.5 inches. Therefore, the volume of the pyramid is (1/3) * 36 sq in * 10.5 in = 126 cubic inches.

2. Prism volume: The volume of a rectangular prism is the length x width x height. We need to find a prism with a volume of 126 cubic inches. Trying out the options:

Option A: 6 inches x 6 inches x 9 inches = 324 cubic inches (too large)

Option B: 6 inches x 9 inches x 6 inches = 126 cubic inches (perfect)

Therefore, the rectangular prism that Jordan should insert the pyramid into is option B, with the dimensions 6 inches by 9 inches by 6 inches. This is because the volume of this prism is equal to the volume of the pyramid, which satisfies the condition for proving the formula.