A hollow garden roller 63 cm wide with a girth of 440 cm is made of iron 4 cm thick. The volume of the iron used is :

1. 154982 cm³

2. 106372 cm³

3. 107812 cm³

4. 107712 cm³

Length of the roller (h) = 63 cm

Let external radius be R cm and internal radius be r cm.

Girth of the roller = Circumference of roller = 440 cm

⇒ 2πR = 440

$\Rightarrow 2 \times \dfrac{22}{7} \text{R} = 440 \\[1em] \Rightarrow \dfrac{44}{7} \text{R} = 440 \\[1em] \Rightarrow \text{R} = 440 \times \dfrac{7}{44} \\[1em] \Rightarrow \text{R} = \dfrac{3080}{44} \\[1em] \Rightarrow \text{R} = 70 \text{ cm.}$

Thickness = External radius (R) - internal radius (r)

⇒ 4 = 70 - r

⇒ r = 70 - 4 = 66 cm

External volume = πR²h

$= \dfrac{22}{7} \times (70)^2 \times 63 \\[1em] = 22 \times 4900 \times 9 \\[1em] = 970200$

Internal volume = πr²h

$= \dfrac{22}{7} \times (66)^2 \times 63 \\[1em] = 22 \times 4356 \times 9 \\[1em] = 862488$

Volume of iron = External volume - Internal volume

= 970200 - 862488

= 107712 cm³

Hence, option 4 is the correct option.