Find the weight of a solid cone whose base is of diameter $14\ cm$ and vertical height $51\ cm$, supposing the material of which it is made weighs 10 grams per cubic cm.

 Given:

The base diameter of a solid cone is $14\ cm$ and its vertical height is $51\ cm$.

The material of which it is made weighs 10 grams per cubic cm.

To do:

We have to find the weight of the solid cone.

Solution:

Diameter of the base of the solid cone $= 14\ cm$

This implies,

Radius of the cone $(r)=\frac{14}{2}$

$=7 \mathrm{~cm}$

Vertical height of the cone $(h) = 51\ cm$

Volume of the cone $=\frac{1}{3} \pi r^{2} h$

$=\frac{1}{3} \times \frac{22}{7} \times 7 \times 7 \times 51$

$=2618 \mathrm{~cm}^{3}$

Weight of $1 \mathrm{~cm}^{3}=10$ grams

Total weight of the solid cone $=2618 \times 10 \mathrm{gm}$

$=\frac{26180}{1000}\ kg$

$=26.180 \mathrm{~kg}$

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Updated on: 10-Oct-2022

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