Eight metallic balls of one centimetre radius each are melted into one ball. The diameter of the new ball is
2 cm
6 cm
4 cm
1 cm
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CAPF – 2021
– The volume of each small ball (radius r=1 cm) is V_small = (4/3)π(1)³ = (4/3)π cubic cm.
– When 8 such balls are melted, the total volume of metal is the sum of their volumes: Total Volume = 8 * V_small = 8 * (4/3)π cubic cm.
– This total volume is melted into a single new ball. Let the radius of the new ball be R. Its volume is V_new = (4/3)πR³.
– Equating the volumes: (4/3)πR³ = 8 * (4/3)π.
– Cancelling (4/3)π from both sides: R³ = 8.
– Taking the cube root: R = ³√8 = 2 cm.
– The question asks for the diameter of the new ball, which is twice the radius: Diameter = 2 * R = 2 * 2 cm = 4 cm.