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# cones

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If a haystack in the shape of a right circular cone has a base radius of 5 meters and contains 12 tons of hay, what will be the number of tons of hay in a similar conical haystack whose base diameter is 15 meters? Two right cones are similar if their heights and their base radii are in proportion. Express your answer as a decimal to the nearest tenth.

Feb 25, 2021

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Base radius $\frac{15}{2}$, multiplying by $\frac{3}{2}$, so height is $12\cdot \frac32=18$.

The volume of a cone is $\pi r^2 \cdot \frac{h}{3}=\pi \cdot \frac{225}{4}\cdot 6=\boxed{\frac{675}{2}\pi}$

Rounded to the nearest tenth it is $\boxed{1060.3}$

Feb 25, 2021
edited by thedudemanguyperson  Feb 25, 2021