# A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel

**Solution:**

The figure drawn below of the vessel and lead shot is to visualize it.

As the water is filled up to the brim in the vessel

Volume of water in the vessel = volume of the conical vessel.

On dropping a certain number of lead shots (sphere) into the vessel one-fourth of the water flows out.

Volume of all lead shots dropped into the vessel = 1/4 × Volume of the water in the vessel

Hence,

Number of lead shots = 1/4 × volume of the water in the vessel ÷ volume of each lead shot

We will find the volume of the water in the vessel and lead shot by using formulae;

Volume of the sphere = 4/3 πr^{3}

where r is the radius of the hemisphere

Volume of the cone = 1/3 πR^{2}h

where R and h are the radius and height of the cone respectively

Height of the conical vessel, h = 8 cm

Radius of the conical vessel, R = 5 cm

Radius of the spherical lead shot, r = 0.5 cm

Number of lead shots = 1/4 × volume of the water in the vessel ÷ volume of each lead shot

= 1 /4 × 1/3 πR^{2}h × 3/4 πr^{3}

= πR^{2}h/12 × 3/4πr^{3}

= R^{2}h / 16r^{3}

= (5cm × 5 cm × 8 cm) / (16 × 0.5 cm × 0.5 cm × 0.5 cm)

= 100

Thus, the number of lead shots dropped in the vessel is 100.

**Video Solution:**

## A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel

### NCERT Solutions for Class 10 Maths - Chapter 13 Exercise 13.2 Question 5 :

A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel

The number of lead shots dropped in the inverted cone-shaped vessel is 100