Question

the height of a cone is 5m. Find the height of another cone whose volume is 16 times its volume and radius equal to its diameter

Answer 1

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Answer 2

Given,

The height of the cone is 5m.

The other cone's volume is 16 times of the present cone.

The radius of the new cone is equal to the diameter of the previous one,

To Find,

The height of the new cone.

Solution,

The volume of old cone = πr²h

According to Question, we can say,

$16.\frac{1}{3} \pi r^{2} h$=$\frac{1}{3} \pi (2r)^{2} h$

⇒$16.\frac{1}{3} .\frac{22}{7} r^{2} 5$=$\frac{1}{3} .\frac{22}{7} 4 r^{2} h$.

⇒$16.\frac{110}{21} r^{2}$=$\frac{88}{21}r^{2} h$.

⇒$16.110r^{2} =88r^{2} h$.

⇒h=$\frac{16.110}{88}$.

⇒h=20.

Hence, the height h of new cone is 20m.