A heap of rice is in the form of a cone of base diameter $24\ m$ and height $3.5\ m$. Find the volume of the rice. How much canvas cloth is required to just cover the heap?
Given: Base diameter, $d=24\ m$ and height, $h=3.5\ m$
To do: To find the volume of the rice and to find that how much cloth is required to cover the heap.
Solution:
Given, base diameter, $d= 24\ m$
Base radius, $r = 12\ m$ $( \because r=\frac{d}{2})$
Height $= 3.5\ m$
Volume of the cone $=\frac{1}{3}\times\pi r^{2}h$
$=\frac{1}{3}\times\ \frac{22}{7}\times12\times12\times3.5$
$=528\ cubic\ meter$
slant height of cone, $l=\sqrt{r^{2}+h^{2}}$
$=\sqrt{12^{2}+3.5^{2}}$
$=\sqrt{144+12.25}$
$=\sqrt{152.25}$
$ =12.5\ m$
Curved surface Area of the heap $=\pi rl$
$=\frac{22}{7}\times12\times12.5$
$=471.42 m^{2}$
Hence the volume of the rice heap is $528\ m^{3}$ and $471.42\ m^{2}$ cloth is required to cover the heap.
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