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 cm³ of iron is 8 gm.
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Answer:
The mass of the iron pole = 102.2 kg
Step-by-step explanation:
SOLUTION :
Given :
Base diameter of the cylindrical portion = 12 cm
Radius of the cylinder & cone ,r = 12/2 = 6 cm
Height of the cylinder , H = 110 cm
Height of the cone, h = 9 cm
Volume of the pole, V = Volume of the cylinder + Volume of the cone
V = πr²H + ⅓ πr²h
V = πr²(H + 1/3h)
V = π6²(110 + ⅓ × 9)
V = 36π(110 + 3)
V = 36 × 22/7 × 113
V = 89496/7
Volume of the pole,V = 12,785.14 cm³
Mass of 1 cm³ of the iron pole = 8 gm
Mass of 12785.14 cm³ of the iron pole = 8 × 12785.14
= 102281.12 gm
= 102281.12/1000 kg
[1 g = 1/1000 kg]
Mass of the iron pole = 102.2 kg
Hence, the mass of the iron pole = 102.2 kg
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