A cone,a hemisphere,and a cylinder stand on e | vedclass

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Question

(A) Let the radius of the base be $r$. Since they have the same height,the height of the cone and the cylinder is $h = r$. $1$. Volume of the cone: $V

Vedclass · Accepted Answer

$1: 2: 3$

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(A) Let the radius of the base be $r$. Since they have the same height,the height of the cone and the cylinder is $h = r$. $1$. Volume of the cone: $V_1 = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi r^2 (r) = \frac{1}{3} \pi r^3$. $2$. Volume of the hemisphere: $V_2 = \frac{2}{3} \pi r^3$. $3$. Volume of the cylinder: $V_3 = \pi r^2 h = \pi r^2 (r) = \pi r^3$. Ratio $V_1 : V_2 : V_3 = \frac{1}{3} \pi r^3 : \frac{2}{3} \pi r^3 : \pi r^3$. Dividing by $\frac{1}{3} \pi r^3$,we get the ratio $1 : 2 : 3$.

$A$ cone,a hemisphere,and a cylinder stand on equal bases and have the same height. The ratio of their volumes is:

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