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Doubling both the area of the bases and the height of a prism doubles its volume. T/F

2 Answers

5 votes

Answer:

True.

Step-by-step explanation:

User Vlad Khomich
by
7.7k points
1 vote

Answer: False

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Step-by-step explanation:

Let's consider a prism that has dimensions of

  • L = 3 ft
  • W = 4 ft
  • H = 5 ft

and we'll say that the base is a rectangle with length L and width W. The area of the base is L*W = 3*4 = 12 sq ft. The volume of this prism is L*W*H = 3*4*5 = 60 ft^3

If we double the area of the base, then we go from 12 ft^2 to 24 ft^2. If we double the height, then we go from 5 ft to 10 ft.

The new volume of this larger prism is (area of base)*(height) = (24)*(10) = 240 ft^3

The jump from 60 ft^3 to 240 ft^3 is not "times 2". Instead, the multiplier is 240/60 = 4. This example shows that the volume has been quadrupled.

User TheLazyFox
by
7.7k points

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