Question

A heap of wheat is in the form of cone of diameter 9 m and height 3.5 m . Find volume.How much canvas cloth is required to just cover the heap?$(Use\pi =\mathrm{3.14.})$

Answer 1

Given : Diameter = 9 m or radius =9/2 = 4.5 m and h = 3.5 m
Volume of cone = $\frac{13}{\pi }{r}^{2}h$
= $\frac{13}{\times }\frac{22}{7}\times 4.5\times 4.5\times 3.5$
= $\frac{1559.25}{21}$
Volume of the cone = 74.25 cu m
Just to cover the heap, we have to find the curved surface area of the cone. For slant height 'l' is needed.
So, $l={\sqrt{r}}^2+h^2$
$l=\sqrt{4}{.5}^2+{3.5}^2$
$l=\sqrt{2}0.25+12.25$
$l=\sqrt{3}2.5$
l = 5.7008 m
Curved surface area of the cone =$\pi rl$
= $\frac{22}{7}\times 4.5\times 5.7008$
= 564.3792/7
CSA of the cone = 80.6256 $m^2$
So, area of the canvas required to cover the heap of wheat is 80.6256 sq m