How many small solid spheres each of 5 mm radius can be made out of a metallic solid cone whose base has radius 21 cm and height 30 cm ?
Answer & explanation
Correct answer: option 2
We know that,
The volume of a sphere = \(\frac{4}{3}\) × π × (radius)3
The volume of a cone = \(\frac{1}{3}\) × π × (radius)2 × height
We have,
The radius of the cone = 21 cm = 210 mm
The height of the cone = 30 cm = 300 mm
The radius of the sphere = 5 mm
Let, the number of sphere required = n
So, n × \(\frac{4}{3}\) × \(\frac{22}{7}\) × (5)3 = \(\frac{1}{3}\) × \(\frac{22}{7}\) × (210)2 × 300
n × \(\frac{4}{3}\) × \(\frac{22}{7}\) × 125 = \(\frac{1}{3}\) × \(\frac{22}{7}\) × 44100 × 300
n × 4 × 125 = 44100 × 300
n = 26460