Question

section b: practice problems

1. andre and clare used different strategies to find the volume of this rectangular prism.

a. andre says the volume of this rectangular prism is 8×24 cubic units. explain or show why andre is correct.
b. clare says the volume of the rectangular prism is 6×32 cubic units. explain or show why clare is also correct.

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular - prism is $V = l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height.

Step2: Analyze Andre's statement

If we consider the base of the rectangular prism with dimensions $6$ units and $4$ units, the area of the base $B=6\times4 = 24$ square units. The height of the prism is $l = 8$ units. Using the volume formula $V=B\times h$, we get $V=8\times24$ cubic units. So Andre is correct.

Step3: Analyze Clare's statement

If we consider the base of the rectangular prism with dimensions $8$ units and $4$ units, the area of the base $B = 8\times4=32$ square units. The height of the prism is $w = 6$ units. Using the volume formula $V = B\times h$, we get $V=6\times32$ cubic units. So Clare is correct.

Answer:

a. Andre is correct because if we take the base with sides 6 and 4 (area of base = 6×4 = 24) and height 8, using V = Bh, the volume is 8×24 cubic units.
b. Clare is correct because if we take the base with sides 8 and 4 (area of base = 8×4 = 32) and height 6, using V = Bh, the volume is 6×32 cubic units.