A heap of rice in the form of a cone of diameter $ 9 \mathrm{~m} $ and height $ 3.5 \mathrm{~m} $. Find the volume of rice. How much canvas cloth is required to cover the heap?

Given:

A heap of rice in the form of a cone of diameter \( 9 \mathrm{~m} \) and height \( 3.5 \mathrm{~m} \).

To do:

We have to find the volume of rice and the area of the canvas cloth required to cover the heap.

Solution:

Height of the heap of rice cone $h = 3.5\ m$

Diameter of the cone $= 9\ m$

Radius of the cone $r =\frac{9}{2}\ m$

This implies,

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

$=\frac{1}{3} \times \frac{22}{7} \times (\frac{9}{2})^2 \times 3.5$

$=\frac{6237}{84}$

$=74.25 \mathrm{~m}^{3}$

Slant height of the cone $l=\sqrt{r^{2}+h^{2}}$

$=\sqrt{(\frac{9}{2})^{2}+(3.5)^{2}}$

$=\sqrt{\frac{81}{4}+12.25}$

$=\sqrt{\frac{130}{4}}$

$=\sqrt{32.5}\ m$

Canvas cloth required to cover the heap of rice $=$ Curved surface area of the heap of rice

$=\pi r l$

$=\frac{22}{7} \times r \times l$

$=\frac{22}{7} \times \frac{9}{2} \times \sqrt{32.5}$

$=\frac{11 \times 9}{7} \times 5.7$

$=14.14\times5.7$

$=80.61 \mathrm{~m}^{2}$

Hence, \( 80.61 \mathrm{~m}^{2} \) of canvas cloth is required to just cover the heap.

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Updated on: 10-Oct-2022

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