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What is the volume of prism B if it is the same height as prism A and every cross-sectional area of prism A is equal to every cross-sectional area of prism B at the same level?

A) 210 in³
B) 360 in³
C) Impossible to tell
D) 630 in³
E) 60 in³

1 Answer

2 votes

Final answer:

The volume of prism B is impossible to determine without the specific measurement of L in inches for prism A. Since both prisms have identical cross-sectional areas at corresponding levels and heights, their volumes would be the same. However, we can't calculate it without knowing the value of L.

Step-by-step explanation:

The volume of prism B is the same as the volume of prism A if every cross-sectional area of prism A is equal to every cross-sectional area of prism B at the same level and they have the same height. Since the volume of a prism is the product of the cross-sectional area and the height, and both prisms have identical height and cross-sectional areas at corresponding levels, they will have the same volume.

Given that Block A has a volume of L x 2L x L, which equals 2L³, and Block B is 4 times larger in volume, thus Block B's volume is 2L³ times 4, which is 8L³. Since the volume of Block, A is given as 21 in³ (assuming there's a typo and it should be 2L³ and equals 10.5 in³), the volume of Block B would be 4 times 21 in³, resulting in 84 in³. However, based on the information provided, and assuming no other typo, we cannot find the exact numerical volume of Block B, since the base L in inches is not given. Therefore, the correct answer is C) Impossible to tell.

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