Question

A cylindrical jar of radius 12 cm contains orange juice to a depth of 20 cm.A child drops an orange into the jar and the level of juice rises by 6.75 cm. What is the radius of the orange, if it is the shape of a complete sphere? Find the surface area of the sphere.

Answer 1

given that 
in the cylinder
radius = 12 cm
height = 20 cm
volume of the cylinder = πr²h
= π × 12 × 12 × 20
after the orange is thrown 
in the cylinder
radius = 12 cm
height = 26.75 cm
volume of the cylinder = π × 12 × 12 × 26.75
then 
the volume of the sphere = volume of the cylinder of second - volume of the cylinder
= π ×12×12×26.75 - π×12×12×20
= π×12×12(26.75 - 20)
= π×12×12×6.75
volume of the sphere = π×12×12×6.75
4/3 πr³ = π×12×12×6.75
r³ = 729
r = 9 cm    
the radius is 9 cm
surface area of the sphere = 4 π r²
= 4 × 22/7 × 9 × 9
=  1018.285 cm²