Question

Use the image to answer the question.

A shaded cone has the following labeled dimensions: the height is 9 feet, and the diameter of the base is 8 feet.

Compare the original volume of the cone with the volume of the cone if it were dilated using a scale factor of 14
.

(1 point)
Responses

The original volume of the cone is 48π
and the dilated volume is much smaller, 3π
.
The original volume of the cone is 48 pi and the dilated volume is much smaller, 3 pi .

The original volume of the cone is 12π
and the dilated volume is much smaller, 34π
.
The original volume of the cone is 12 pi and the dilated volume is much smaller, Start Fraction 3 over 4 End Fraction pi .

The original volume of the cone is 48π
and the dilated volume is much smaller, 34π
.
The original volume of the cone is 48 pi and the dilated volume is much smaller, Start Fraction 3 over 4 End Fraction pi .

The original volume of the cone is 12π
and the dilated volume is much smaller, 98π
.
The original volume of the cone is 12 pi and the dilated volume is much smaller, Start Fraction 9 over 8 End Fraction pi .
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Answer 1

Original: V = (1/3)πr^2h = (1/3)π(4^2)(9) = 48π.

With scale factor 1/4, volume scale = (1/4)^3 = 1/64, so dilated volume = 48π·(1/64) = 3/4 π.

So: original 48π and dilated 3/4 π.