Question

A sphere and a cone both are melted.They have the same base radius of 8cm.If the number of spheres made by melting both are 44 and the radius of each sphere is 4cm,find the height of the cone

Answer 1

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Answer 2

The height of the cone is 144 cm.

Step-by-step explanation:

Consider the provided information.

A sphere and a cone both are melted. They have the same base radius of 8cm.

Total volume = Volume of sphere + Volume of cone

Total volume = $\frac{4}{3}$πr³ + $\frac{1}{3}$πr²h

Substitute the respective values.

$\text{Total volume}=\frac{4}{3}\pi\times8^3+\frac{1}{3}\pi\times8^2h\\\\\text{Total volume}=\frac{2048\pi}{3}+\frac{64\pi h}{3}$

The number of spheres made by melting both are 44 and the radius of each sphere is 4 cm.

Volume of 44 spheres are: $V=44\times\frac{4}{3}\pi\times4^3$

Volume of 44 spheres must be same as the volume of cone and sphere.

$\frac{2048\pi}{3}+\frac{64\pi h}{3}=44\times\frac{4}{3}\pi\times4^3\\2048+64h=44\times4\times64\\2048+64h=11264\\64h=9216\\h=144$

Hence, the height of the cone is 144 cm.

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