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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 cm3of iron is 8 gm.
Solution
Let r1 cm and r2 cm denate the radii of the base of the cylinder and cone respectively. then,
r1 = r2 = 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 cm3
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 cm3
Mass of 1 cm3 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.
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