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Question
A hollow garden roller of 42 cm diameter and length 152 cm is made of cast iron 2 cm thick. Find the volume of iron used in the roller.
Solution
Diameter of the hollow garden roller = 42 cm
∴ Inner radius = `42/2` = 21 cm ...`[∵ "Radius" = ("Diameter")/2]`
∴ Thickness of cast iron = 2 cm
∴ Outer radius = 21 + 2 = 23 cm
Volume of hollow cylinder = π(R2 – r2) × h ...[Where, R is outer-radius and r is inner-radius]
= `22/7 xx [(23)^2 - (21)^2] xx 152`
= `22/7 xx (529 - 441) xx 152`
= `22/7 xx 88 xx 152`
= `(22 xx 88 xx 152)/7`
= `294272/7`
= 42038.85 cm3
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