Question

A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylindrical part is `4 2/3` m and the diameter of hemisphere is 3.5 m. Calculate the capacity and the internal surface area of the vessel. 

Answer 1

 
Diameter of the base = 3.5 m

Therefore, radius =`3.5/2 m = 1.75 m = 7/4 m` 

Height of cylindrical part = `4 2/3 = 14/3 m `

(i) Capacity (volume) of the vessel

= `pir^2h + 2/3pir^3`

= `pir^2(h + 2/3r)` 

= `22/7 xx 7/4 xx 7/4(14/3 + 2/3 xx 7/4)` 

= `77/8(14/3 + 7/6)` 

= `77/8((28 + 7)/6)` 

= `77/8 xx 35/6` 

= `2695/48` 

= 56.15 m³ 

(ii) Internal curved surface area

= `2pirh + 2pir^2 = 2pir(h + r) ` 

= `2 xx 22/7 xx 7/4(14/3 + 7/4)` 

= `11((56 + 21)/12)` 

= `11 xx 77/12` 

= `847/12`

= 70.58 m²