Question

A heap of wheat is in the form of a cone whose diameter is $10.5m$ and height is $3m$. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

Answer 1

Given:

$\Rightarrow$Diameter $=10.5$ m

$\Rightarrow$radius $=r$ $=5.25$ m

$\Rightarrow$height $=3$ m

$\Rightarrow$volume $=\frac{1}{3}\pi r^{2}h$

$\Rightarrow$Volume$=(\frac{1}{3}\times \frac{22}{7}\times 5.25\times 5.25\times 3)$ $m^3$

$\Rightarrow$Volume$=86.625m^3$

For slant height:

$\Rightarrow$$l^2=h^2+r^2=3^2+(5.25{)}^2$

$=9+27.5625=36.5625$

$\Rightarrow 6.0467$ m(approx)

Canvas needed to protect wheat from rain

Therefore, curved surface area$=\pi rl$
$=(227\times 5.25\times 6.0467)$ $m^2$

$=99.77$ $m^2$(approx)