Mathematics

A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm³ of iron has approximately 8g mass. (Use π = 3.14)

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The below figure shows the solid iron pole consisting of the two cylinders:

Given,

For bigger cylinder :

Diameter (d) = 24 cm

Radius (R) = $\dfrac{d}{2} = \dfrac{24}{2}$ = 12 cm.

Height (H) = 220 cm

Volume = πR²H

= 3.14 × (12)² × 220

= 3.14 × 144 × 220

= 99475.20 cm³

For smaller cylinder :

Radius (r) = 8 cm

Height (h) = 60 cm

Volume = πr²h

= 3.14 × 8² × 60

= 3.14 × 64 × 60

= 12057.60 cm³.

Volume of pole = Volume of bigger cylinder + Volume of smaller cylinder

= 99475.20 + 12057.60 = 111532.80 cm³

Given,

1 cm³ of iron weighs 8 g.

∴ Mass of pole = Volume of pole × 8 g

= 111532.80 × 8 = 892262.4 g = $\dfrac{892262.4}{1000}$ = 892.26 kg.

Hence, mass of pole = 892.26 kg.

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