A solid metallic spherical ball is melted to make 250 identical solid metallic hemispherical balls. If the original metallic ball requires 10 litres of colour to be painted on its surface, then ___________ litres of colour would be required to paint all the 250 hemispherical balls
Answers
Given :
A solid metallic spherical ball is melted to make 250 identical solid metallic hemispherical balls.
original metallic ball requires 10 litres of colour to be painted
To Find :
How much paint will be required to paint 250 metallic solids
Solution:
•let radius of sphere is R & Radius of hemisphere is r
•Since metallic solid sphere is melted to form 250 hemispherical solids then Amount of metal will be same in both cases
=> 4πR³/3 = 250 × 2πr³/3
=> R³ = 125 r³
=> R = 5r
=> r = R/5
Now, surface area of solid spherical
ball is 4πR²
Surface area of = 3πr²
hemispherical solid
Surface area of = 3π(R/5)²
hemispherical solid
Surface area of = 3πR²/25
hemispherical solid
Surface area of 250 = 30πR²
hemispherical solid
•Now , 10 litres of paint is required to paint 4πR²
therefore , to paint 30πR² area 75 litres of paint will be required.
•Hence , To paint 250 hemispherical balls 75 litres of paint is required