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 cm³ of iron is 8 gm.

Answer 1

Given radius of cylindrical part(r) = \(\frac{12}2\) = 6 cm 

Height of cylinder (h) = 110 cm 

Length of cone (l) = 9 cm 

Volume of cylinder = πr²h

 V₁= π (6)² 110 cm³

Volume of cone = \(\frac{1}3\)πr²l

V₂ = \(\frac{1}3\)π(6)²9

=108 π cm³ 

Volume of pole = v₁ + v₂ 

= π (6)²110 +108 π

= 12785.14 108 cm³ 

Given mass of 1 cm³ of iron = 8 gm 

Mass of 1275.14 cm³ of iron = 12785.14 × 8 

= 102281.12 

= 102.2 kg 

∴ Mass of pole for 12785.14 cm³ of iron is 102.2 kg