Question

In a field, dry fodder for the cattle is heaped in a conical shape. The height of the cone is 2.1m. and diameter of base is 7.2 m. Find the volume of the fodder. if it is to be covered by polythin in rainy season then how much minimum polythin sheet is needed ?
($\mathrm{\pi }=\frac{22}{7}$ and $\sqrt{17.37}=4.17$).

Answer 1

Height of the conical heap of fodder, h = 2.1 m

Radius of the conical heap of fodder, r = $\frac{7.2}{2}$ = 3.6 m

∴ Volume of the fodder = $\frac{1}{3}\mathrm{\pi }{r}^{2}h=\frac{1}{3}\times \frac{22}{7}\times {\left(3.6\right)}^2\times 2.1$ = 28.51 m³ (Approx)

Let the slant height of the conical heap of fodder be l m.

$$\begin{gathered} \therefore l^2=r^2+h^2 \\ \Rightarrow l^2={\left(2.1\right)}^2+{\left(3.6\right)}^2 \\ \Rightarrow l^2=4.41+12.96=17.37 \\ \Rightarrow l=\sqrt{17.37}=4.17\mathrm{m} \end{gathered}$$
∴ Minimum area of the polythin needed to cover the fodder = $\mathrm{\pi }$rl = $\frac{22}{7}\times 3.6\times 4.17$ = 47.18 m² (Approx)

Thus, the volume of the fodder is 28.51 m³ and the minimum area of the polythin needed to cover the fodder in rainy season is 47.18 m².