Question

A right rectangular prism has a height of 15 in, and the area of the cross section taken parallel to the base at a level of 5 in above the base is 25 in2. A right triangular prism has a height of 15 in, and the area of the cross section taken parallel to the base at a level of 5 in above the base is 25 in2. Do the solids have the same volume?

A.
Yes, because they have the same height and the same cross-sectional area at every level parallel to the bases.
B.
Yes, because the solids are congruent.
C.
No, because the heights are not equal.
D.
No, because the cross-sectional area at every level must be the same, not just at one level.

Answer 1

Answer with explanation:

Volume of Right Rectangular prism, having height =15 inches,and the area of the cross section taken parallel to the base at a level of 5 in above the base is 25 in²= Area of Base × Height

= 25×5

=125 inches³

Similarly, Area of right triangular prism has a height of 15 in, and the area of the cross section taken parallel to the base at a level of 5 in above the base is 25 in²

= Area of Base × Height

= 25×5

=125 inches³

Option A:→ Yes, because they have the same height and the same cross-sectional area at every level parallel to the bases.

Answer 2

Answer:A. Yes, because they have the same height and the same cross-sectional area at every level parallel to the bases.

A right prism has constant cross-sectional area at every level parallel to the base and the volume is the area of the base times the height.