#### Question

A solid iron pole having cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole, given that the mass of 1 cm^{3}of iron is 8 gm.

#### Solution

Let r_{1} cm and r_{2} cm denate the radii of the base of the cylinder and cone respectively. then,

r_{1} = r_{2} = 12/2 = 6 cm

let h and l cm be the heights of the cylinder and the cone respectively Then,

h = 110cm and l = 9cm

∴ volume of the cylinder = `pir_1^2h cm^3`

= π x 6 x 6 x 110 cm^{3}

of the cone = `1/3pir_2^2l cm^3`

`1/3xxpixx6xx6xx9`

∴ Total volume of the iron = volume of the cylinder + volume of the cone

= π x 6 x 6 x 110 +1/3 x π x 6 x 6 x 9

= π x 36`((330+9))/3`

= π x 12 x (330+9)

= `22/7xx12xx339`

= 12785.14 cm^{3}

Mass of 1 cm^{3} of iron is 8 gm.

Therefore mass of the iron

= 12785.14 x 8 gm

= 102281.18

102.28 kg.

Hence, the mass of pale is 102.28 kg.