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A spherical glass vessel has a cylindrical neck $7 cm$ long, $4 cm$ in diameter, the diameter of the spherical part is $21 cm$ . What is the quantity of water it can hold taking $π = 227$ ?

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4039 cm 3

4830 cm 3

4939 cm 3

3939 cm 3

answer is C.

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Detailed Solution

Given that a cylindrical neck

7 cm

long,

4 cm

in diameter and the diameter of the spherical part is

21 cm

.
Volume of a sphere =

43 π r 3

Volume of a cylinder

= π r 2 h

The Volume of the spherical Part,
If diameter is 21 cm then,

r = Diameter 2 = 212 = 10.5 cm

Volume of the Spherical Part will be,
=

43 × 227 × (10.5) 3

4851 cm 3

The Volume of the cylindrical neck,
If the diameter is 4cm then,

r = Diameter 2 = 42 = 2 cm

Volume of the Cylindrical Neck will be,

= 227 × (2) 2 × 7

= 88 cm 3

Quantity of water a spherical glass vessel can hold = Volume of spherical part + Volume of cylindrical neck

4851 c m 3 +88 c m 3 = 4939 c m 3

Thus, the spherical glass vessel will hold

4939 cm 3

of water.
Therefore the correct option is 3.

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