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A complete iron pole consists of a 220 cm tall cylinder with a 24 cm base diameter, which is topped by a 60 cm tall cylinder with an 8 cm radius. Given that 1 centimetre of iron weighs roughly 8g, calculate the mass of the pole. (Use $π$ = 3.14)

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888.26 kg

890.26 kg

892.26 kg

894.26 kg

answer is C.

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Detailed Solution

Given that the height of the cylinder = 220 cm and base diameter = 24cm.
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24

Volume of pole = Volume of small cylinder + Volume of large cylinder
Volume of small cylinder =

π r 2 h

Radius = r = 8cm
Height = h = 60cm

⇒ V o l u m e = 3.14 × 82 × 60

⇒ V o l u m e = 3.14 × 64 × 60

⇒ V o l u m e = 12057.6 c m 3 … … (1)

Now,
Height of cylinder = h = 220cm

Radius = r = D i a m e t e r 2

R a d i u s = 242

Radius =12cm
Volume of large cylinder

= π r 2 h ....

(2)

⇒ V o l u m e = 3.14 × 122 × 220

⇒ V o l u m e = 3.14 × 144 × 220

⇒ V o l u m e = 99475.2 c m 3

Volume of pole = Volume of small cylinder + Volume of large cylinder

⇒ V o l u m e = 12057.6 c m 3 + 99475.2 c m 3

Volume of pole =

111532.8 c m 3

1 c m 3

Iron has 8g mass.
So, Mass of

1 c m 3

of iron = 8g
Mass of

111532.8 c m 3

of iron

= 111532.8 × 8 g

Mass of

111532.8 c m 3

of iron =892262.4g

⇒ M a s s o f i r o n = 892262.4 1000 kg

⇒ M a s s o f i r o n = 892.2624 k g

⇒ M a s s o f i r o n = 892.26 k g

Therefore, mass of the iron pole is 892.26 kg.
Therefore the answer is option (3).

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