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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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