The second wedge has a greater volume and it is greater by 4.125 in³.
Volume of each wedge
Since the each cheese wedge has a triangular base, its volume V = 1/2bhw where
- b = length of base of triangle,
- h = height of triangle and
- w = thickness of wedge
Volume of first wedge
Given that for the first wedge, b = 2.5 in, h = 4.5 in and w = 3 in, its volume V' = 1/2bhw
= 1/2 × 2.5 in × 4.5 in × 3 in
= 33.75 in³/2
= 16.875 in³
Volume of second wedge
Given that for the second wedge, b = 3 in, h = 4 in and w = 3.5 in, its volume V" = 1/2bhw
= 1/2 × 3 in × 4 in × 3.5 in
= 42 in³/2
= 21 in³
Since V" = 21 in³ > V' = 16.875 in³, the second wedge has a greater volume.
Amount it is greater by
The amount its is greater than the first volume is the difference in their volumes. V" - V' = 21 in³ - 16.875 in³
= 4.125 in³
The second wedge has a greater volume and it is greater by 4.125 in³.
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