Question

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

Answer 1

Answer:

True.

Step-by-step explanation:

Answer 2

Answer: False

==========================================================

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.