The height of a cone is 30 , cm. A small cone | vedclass

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(B) Let $H = 30 \, cm$ be the height of the larger cone and $h$ be the height of the smaller cone.Let $V$ be the volume of the larger cone and $v$ be

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(B) Let $H = 30 \, cm$ be the height of the larger cone and $h$ be the height of the smaller cone.Let $V$ be the volume of the larger cone and $v$ be the volume of the smaller cone.Since the smaller cone is cut by a plane parallel to the base,the smaller cone and the larger cone are similar.Therefore,the ratio of their volumes is equal to the cube of the ratio of their heights:$\frac{v}{V} = \left( \frac{h}{H} \right)^3$Given $\frac{v}{V} = \frac{1}{27}$,we have:$\frac{1}{27} = \left( \frac{h}{30} \right)^3$Taking the cube root on both sides:$\frac{1}{3} = \frac{h}{30}$$h = \frac{30}{3} = 10 \, cm$The section is made at a height above the base equal to the difference between the height of the larger cone and the height of the smaller cone:Height above base $= H - h = 30 - 10 = 20 \, cm$.

The height of a cone is $30 \, cm$. $A$ small cone is cut off at the top by a plane parallel to the base. If its volume is $\frac{1}{27}$ of the volume of the given cone,at what height above the base is the section made? (in $cm$)

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