Question

A Heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Answer 1

Hope it helps u mate

Answer 2

Height of the cone (h) = 3.5 m

Diameter of the cone = 9 m

Radius of cone $\bold{(r) = \frac {9}{2}m }$

So , volume of rice heap

$= \frac {1}{3} \pi \times r²h \\\\\ = \frac {1}{3} \times \frac{22}{7} \times \frac {9}{2} \times {9}{2} \times {3.5} \\\\\ = \frac {6237}{84}=74.25~m³$

Now , canvas cloth required to just cover heap of rice

$\implies$ Surface area of a rice heap

$= \bold{\pi r l} \\\\\ = \frac {22}{7} \times r \times \sqrt{r²+h²} \\\\\ = \frac {22}{7} \times \frac{9}{2} \times \sqrt{({\frac{9}{2})²}} + (3.5)² \\\\\ = \frac {11 \times 9}{7} \times \sqrt {{\frac{81}{4}+12.25}} \\\\\ = \frac{99}{7} \times \sqrt {\frac{130}{4} = \frac{99}{7}} \times \sqrt{32.5} \\\\\ = 14.142 \times 5.7 \\\\\ = 80.61~m²$

Hence , $80.61~m²$ canvas cloth is required to cover the heap .