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)

detailed solution

1

The figure drawn below is to visualize the iron pole.

We can see that,

 Volume of the solid iron pole = volume of larger cylinder + volume of smaller cylinder

Mass of iron in the pole = 8 g × volume of the solid iron pole in cm³

We will find the volume of the solid by using formula;

Volume of the cylinder = πr²h where r and h are the radius and height of the cylinder respectively

Radius of larger cylinder, R = 24 cm/2 = 12cm

height  of larger cylinder H = 220 cm

Radius of smaller cylinder, r = 8 cm

Height of smaller cylinder, h = 60 cm

Volume of the solid iron pole = volume of larger cylinder + volume of smaller cylinder

= πR²H + πr²h

= π(12 cm × 12 cm × 220 cm + 8 cm × 8 cm × 60 cm)

= 3.14 × (31680 cm³ + 3840 cm³)

= 3.14 × 35520 cm³

= 111532.8 cm³

Mass of 1 cm³ iron is 8 g.

Mass of iron in the pole = 8 g × volume of the solid iron pole 

= 8 g × 111532.8

= 892262.4 g

= 892262.4/1000 kg

= 892.2624 kg

Thus, the mass of iron in the pole is 892.26 kg.