A cylindrical tub if radius 5cm and length 9.8cm is full of water .A solid in the form of a right circular cone mounted on a hemisphere is immersed into the tub.If the radius of the hemisphere is 3.5cm and the total height of the solid ids 8.5cm ,find the volume of water left in the tube

Answer

`= 616 cm^3`

Explanation

Radius of the cylinder r=5 cm
Height of the cylindre , h= 9.8 cm
Radius of the hemisphere R= 3.5cm
Radius of the cone
= radius of the hemiphere
`=3.5 cm = 7/2 cm.`
Height of the cone ,H= (8.5 - 3.5 ) cm = 5 cm
Volume of the water in the cylindrical tub
`= pi r^2 h= (22/7xx5xx5xx9.8)cm^3 = 770 cm^3`
Volume of the soild immersed in the tub
`=2/3piR^3 + 1/3piR^2H`
`[(2/3xx22/7xx7/2xx7/2xx7/2)+(1/2xx22/7xx7/2xx5)]cm^3`
`=(539/6+385/6)cm^3 =(924/6)cm^3=154 cm^3`
`therefore ` volume of water left in the tub `=(770 - 154) cm^3 = 616 cm^3`