Question

A heap of rice is in the form of a cone of base diameter $24$, and height $3.5m$. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

Answer 1

Given that

A heap of rice is in the form of a cone

Diameter $=d=24m$

Radius $=r=\frac{d}{2}=12m$

Height $=h=3.5m$

Volume of Cone $=V=\frac{\pi r^{2}h}{3}$

$V=\frac{\frac{22}{7}\times {12}^2\times 3.5}{3}$ $m^3$

$V=\frac{\frac{22}{7}\times 144\times 3.5}{3}$ $m^3$

$V=528$ $m^3$

Given that canvas cloth is required to just cover the heap

It covered the only curved surface area of Cone

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

$l=\sqrt{{3.5}^2+{12}^2}$ $m$

$l=\sqrt{12.25+144}$ $m$

$l=\sqrt{156.25}$ $m$

$l=12.5$ $m$

Curved surface area of Cone $S=\pi rl$

$S=\frac{22}{7}\times 12\times 12.5$ $m^2$

$S=471.42$ $m^2$