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.
 

Updated on: 10-Oct-2022

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