The shape of a heap of wheat is a right circular cone, the diameter of base of which is 9 metres and height is 3.5 metres. Find the volume of the heap of wheat. How much sq-metre of plastic sheet will be needed to cover that heap of wheat ? [Given that `pi=3.14` and `sqrt(130)=11.4`].

Explanation

The radius of the heap of wheat `=(9)/(2)` metres.
Height `=3.5` metres.
`therefore` the volume of the heap of wheat `=(1)/(3)xx pi xx ((9)/(2))^2xx3.5` cubic - metres.
`=(1)/(3)xx3.14xx(4.5)^2xx3.5` cubic - metres.
`=74.18` cubic - metres.
If the slant height of the heap of wheat be l metre, then
`l^2=(3.5)^2+((9)/(2))^2=((7)/(2))^2+((9)/(2))^2=(49)/(4)+(81)/(4)=(130)/(4)`
`therefore l =sqrt((130)/(4))=5.7` (approx.).
`therefore` the curved surface area of the heap of wheat
`= pi xx (9)/(2)xx5.7sq-m . =3.14xx4.5xx5.7sq-m=80.54sq-m`.
Hence the total volume of the heap of wheat is 74.18 cubic - metres and to cover the heap 80.54 sq-m of plastic sheet will be needed.