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

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 is canvas cloth required to just cover the heap?  (Use π = 3.14).

Solution:

It is given that

Diameter of heap (d) = 9 m

Therefore, Radius of the heap (r)

= d/2

= 9/2 = 4.5 m

Height of the heap (h) = 3.5 m

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

$=1 / 3 * 3.14 * 4.5^{2} * 3.5$

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

Now,

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

$=\sqrt{4.5^{2}+3.5^{2}}=5.70 \mathrm{~m}$

Area to be covered by the cloth = Curved surface area of the heap

$=\pi r l=3.14$ * $4.5$ * $5.70=80.54 \mathrm{~m}^{3}$

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