A solid iron pole consists of a solid cylinder of height 200 cm . . .

Question : A solid iron pole consists of a solid cylinder of height 200 cm and base diameter 28 cm, which is surmounted by another cylinder of height 50 cm and radius 7cm. Find the mass of the pole, given that 1cm³ of iron has approximately 8g mass.

CBSE 2024

Solution : 

Dimensions of Bigger Cylinder 

H = 200 cm 
D = 28 cm
R = D/2 = 28/2 = 14 cm

Dimensions of smaller Cylinder
h = 50 cm 
r = 7 cm 

Volume of the Iron pole  = πR²H+r²h
= π[R²H+r²h]
= 22/7 [(14)²×200+(7)²×50]
= (22/7)×(7)²[2²×200+1²×50]
= 22×7[4×200+50]
= 154×[800+50]
= 154×850
= 130900 cm³

Mass of 1cm³ iron = 8g
Mass of 130900 cm³ iron = 8×130900
= 1047200 g
= [1047200/1000] kg
= 1047.2 kg