# 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, r₁ = 2/2 cm = 1 cm

Radius of spherical part, r₂ = 8.5/2 cm = 4.25 cm

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

= 4/3 πr₂^{3} + πr₁^{2}h

= π [(4/3) r₂^{3} + r₁^{2}h]

= = 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 approximately right while saying that the volume of the glass vessel is 345 cm^{3} which is nearly equal to the actual volume of the glass 346.51 cm^{3}.

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 13

**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 cm³. 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}. The child is approximately correct while saying that the volume of the glass vessel is 345 cm^{3} which is nearly equal to the actual volume 346.51 cm^{3}.

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