Question

A solid is in the form of a right circular cone mounted on a hemisphere. The diameter of the base of the cone, which exactly coincides with hemisphere, is 7 cm and its height is 8 cm. The solid is placed in a cylindrical vessel of internal radius 7 cm and height 10 cm. How much water, in cm³, will be required to fill the vessel completely?

Answer 1

 
Diameter of hemisphere = 7 cm

Diameter of the base of the cone = 7 cm

Therefore, radius (r) = 3.5 cm  

Height (h) = 8 cm

Volume of the solid = `1/3pir^2h + 2/3pir^3`

= `1/3pir^2(h + 2r)` 

= `1/3 xx 22/7 xx 3.5 xx 3.5(8 + 2 xx 3.5)`  

= `77/6(8 + 7)` 

= `385/2` 

= 192.5 cm³  

Now, radius of cylindrical vessel (R) = 7 cm

Height (H) = 10 cm 

∴ Volume = πR²h 

= `22/7 xx 7 xx 7 xx 10` 

= 1540 cm³ 

Volume of water required to fill

= 1540 – 192.5

= 1347.5 cm³