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Question
A cylindrical boiler, 2 m high, is 3.5 m in diameter. It has a hemispherical lid. Find the volume of its interior, including the part covered by the lid.
Solution
Diameter of cylindrical boiler = 3.5 m
∴ Radius (r) = `3.5/2 = 35/20 = 7/4 m `
Height (h) = 2 m
Radius of hemisphere (R) = `7/4 m `
Total volume of the boiler = `pir^2h + 2/3pir^3`
= `pir^2(h + 2/3r)`
= `22/7 xx 7/7 xx 7/4(2 + 2/3 xx 7/4)`
= `77/8(2 + 7/6)`
= `77/8 xx 19/6`
= `1463/48`
= 30.48 m3
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