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?

We have

Given: height of the cone (h) = 2.1 m

Diameter of the base of cone (d) = 7.2 m

⇒ Radius of the base of cone (r) = 7.2/2 = 3.6 m

Volume (V) of the conical fodder is given by,

Volume = πr²h/3

⇒

⇒ V = 28.512

Thus, volume of cone is 28.512 m³.

If it is covered by polythene in rainy season, then it will be covered on the curved surface area, not on the base.

Curved surface area (CSA) of cone is given by,

CSA = πrl …(i)

We need to find l.

In ∆AOB, using Pythagoras theorem,

AB² = AO² + OB²

⇒ l² = 2.1² + 3.6²

⇒ l² = 4.41 + 12.96

⇒ l² = 17.37

⇒ l = √17.37 = 4.17 [given that √17.37 = 4.17]

Substituting l = 4.17 in equation (i),

⇒ CSA = 47.18

Thus, curved surface area of cone is 47.18 m².

Hence, volume of cone is 28.51 m³ and curved surface area of cone is 47.18 m².