A cylindrical vessel with radius 6 cm and height 5 cm is to be made by melting a number of spherical metal balls of diameter 2 cm. The minimum number of balls needed is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 135
In melting the shape we know that the volume will remain constant so we can equate that
The volume of cylinder = number of sphere × the volume of one sphere
The volume of cylinder = πr2h
⇒ π × 62 × 5
⇒ 180π cm3
Volume of one sphere = (4 / 3)πr3
Radius will be = Diameter / 2
⇒ (4 / 3)π × 13
⇒ (4 / 3)π
Number of spheres = 180π / (4 / 3)π
⇒ 135