A heap of wheat is in the form of a cone of diameter $9\ m$ and height $3.5\ m$. Find its volume. How much canvas cloth is required to just cover the heap? (Use $\pi = 3.14$).

 Given:

A heap of wheat is in the form of a cone of diameter $9\ m$ and height $3.5\ m$. 

To do:

We have to find its volume and the canvas cloth required to just cover the heap.

Solution:

Diameter of the conical heap of wheat $= 9\ m$

This implies,

Radius $(r)=\frac{9}{2} \mathrm{~m}$

Height of the conical heap $(h)=3.5 \mathrm{~m}$

$=\frac{7}{2}\ m$

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

$=\frac{1}{3} \times 3.14 \times \frac{9}{2} \times \frac{9}{2} \times \frac{7}{2}$

$=74.18 \mathrm{~m}^{3}$

We know that,

$l^2=r^2+h^2$

$\Rightarrow l=\sqrt{r^{2}+h^{2}}$

$=\sqrt{(\frac{9}{2})^{2}+(\frac{7}{2})^{2}}$

$=\sqrt{\frac{81}{4}+\frac{49}{4}}$

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

$=\frac{\sqrt{130}}{2}$

Curved surface area of the heap $=\pi r l$

$=3.14 \times \frac{\sqrt{130}}{2} \times \frac{9}{2}$

$=3.14 \times \frac{11.4}{2} \times \frac{9}{2}$

$=80.54 \mathrm{~cm}^{2}$

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Updated on: 10-Oct-2022

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