A copper wire of radius 6cm and height 8cm is melted to form spheres of radius 2cm. How many such spheres can be formed?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 27.
A copper wire is in the shape of a cylinder and when we melt any shape into any other, their volume remains same.
Let x be the number of spheres that were formed.
Volume of cylinder = πr2h
Volume of spheres = 4πr3/3
⇒ πr2h = x × (4πr3/3)
⇒ 62 × 8 × 3/4 = x × 23
⇒ 36 × 3/4 = x
⇒ x = 27