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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.
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
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.

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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