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 ?

26460

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