Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.

Class 10 | Cylinder, Cone and Sphere (Surface Area and Volume) | Exercise 20D | ICSE | Selina

Let the radius of the smaller cone be r cm

Diameter of bigger cone = 40 cm

the radius = 20 cm and height = 9 cm

$\begin{array}{*{35}{l}} Volume\text{ }of\text{ }larger\text{ }cone\text{ }=\text{ }1/3\text{ }\pi \text{ x }{{\left( 20 \right)}^{2}}~x\text{ }9 \\ The\text{ }volume\text{ }of\text{ }the\text{ }smaller\text{ }cone\text{ }=\text{ }1/3\text{ }\pi \text{ x }{{r}^{2}}~x\text{ }108 \\ \end{array}$

Volume of larger cone = 3 x Volume of smaller cone

$\begin{array}{*{35}{l}} 1/3\text{ }\pi \text{ x }{{\left( 20 \right)}^{2}}~x\text{ }9\text{ }=\text{ }3\text{ x }\left( 1/3\text{ }\pi \text{ x }{{r}^{2}}~x\text{ }108 \right) \\ {{r}^{2}}~=\text{ }{{\left( 20 \right)}^{2}}~x\text{ }9/\text{ }\left( 108\text{ x }3 \right) \\ r\text{ }=\text{ }20/6\text{ }=\text{ }10/3\text{ }cm \\ \end{array}$

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