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
Answer & explanation
Correct answer: option 4
We know that,
Volume of cylinder = πr2h
Volume of sphere = \(\frac{4}{3}\) πr3
Given data,
Radius of cylindrical vessel R = 6 cm
Height of cylindrical vessel H = 5 cm
Diameter of spherical metal each ball = 2 cm
Radius of each ball r = 1 cm
Let n be the number of balls,
According to the question
n × \(\frac{4}{3}\) × π × 13 = π × 62 × 5
= n = 180 × \(\frac{3}{4}\)
= n = 135