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. 

Answer 1

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