Question

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Answer 1

D. The volume of the square prism is twice the volume of the cylinder

To determine the relationship between the volume of the square prism and that of the cylinder, we need to find both volumes.

The volume of the square prism is V = Ah where A is the cross-sectional area and h its height. Since A = 314 square units,

V = 314 × h = 314h

Also, the volume of the cylinder is V = A'h where A' is the cross-sectional area of the cylinder and h' its height. Since the A' = 50π square units,

V' = 50π × h' = 50πh'

The ratio of the volume of the square prism to that of the cylindrical prism is V/V' = 314h/50πh'

Since the height of the square prism equals that of the cylinder, h = h'.

So, V/V' = 314h/50πh

V/V' = 314/50π

if we take π = 3.14,

V/V' = 314/(50 × 3.14)

V/V' = 100/50

V/V' = 2

So, V = 2V'

Thus, the volume of the square prism is twice the volume of the cylinder.

So, the answer is D.

Learn more about square prisms and cylinders here:

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