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Q.

A hollow garden roller is 63 cm wide with a grit of 440 cm, and is made of 4cm thick iron. Find the volume of iron used.

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a

    217709 cm3

b

    107712 cm3

c

    117566 cm3

d

    184952 cm3 

answer is B.

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Detailed Solution

Given , h=63cm
The outer circumference of the roller is 440 cm
Let’s consider R as the external radius and r as inner radius.
Circumference = 2𝜋R = 440
⇒ 2𝜋R= 440
⇒ 2x

22
xR= 440
7
⇒ R= 440x 7
2×22
⇒ R= 70
Inner radius = r = R-4
⇒ r = R-4
⇒ r = 70-4
⇒ r = 66
Therefore , the inner radius is 66 cm Volume of the iron = 𝜋 (R2-r2) h
V= 22 (702-662)x63 ……[(a2-b2)= (a+b) (a-b)]
7
= 22x544x9
= 107712 cm3.
  
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