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