# A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm^{3}. Check whether she is correct, taking the above as the inside measurements, and π = 3.14

**Solution:**

A figure is drawn below to visualize the glass vessel.

As the glass vessel is a combination of a sphere and a cylinder

Volume of the glass vessel = volume of the spherical part + volume of the cylindrical part

Height of cylindrical part, h = 8 cm

Radius of cylindrical part, r_{1} = 2/2 cm = 1 cm

Radius of spherical part, r_{2} = 8.5/2 cm = 4.25 cm

Volume of the glass vessel = volume of the spherical part + volume of the cylindrical part

= 4/3 πr_{2}^{3} + πr_{1}^{2}h

= π (4/3r_{2}^{3} + r_{1}2h)

= = 3.14 × [4/3 × 4.25 cm × 4.25 cm × 4.25 cm + 1 cm × 1 cm × 8 cm]

= 3.14 × (102.354 cm^{3} + 8 cm^{3})

= 3.14 × 110.354 cm^{3}

= 346.51 cm^{3}

Therefore, the child is wrong while saying that the volume of the glass vessel is 345 cm^{3} as the volume of the glass is 346.51 cm^{3}

**Video Solution:**

## A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm^{3}. Check whether she is correct, taking the above as the inside measurements, and π = 3.14

### NCERT Solutions for Class 10 Maths - Chapter 13 Exercise 13.2 Question 8 :

A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm^{3}. Check whether she is correct, taking the above as the inside measurements, and π = 3.14

The child is wrong while saying that the volume of the glass vessel is 345 cm^{3} as the volume of the glass is 346.51 cm^{3}