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A vessel is in the form of a hemisphere bowl mounted by a hollow cylinder. The diameter of the hemisphere is $16 cm$ and the total height of the vessel is 15cm. What is the capacity of the vessel taking $π = 227$ ?

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1542.09 c m 3

810.167 cm 2

820.177 cm 2

910.267 cm 2

answer is A.

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Detailed Solution

Given that the diameter of the hemisphere is

16 cm

and the total height of the vessel is 15cm.
We have the following formula,
Volume of a hemisphere =

23 π r 3

Radius of hemisphere =

162 = 8 c m

Volume of hemisphere will be,

= 23 π r 3 = 23 × 227 × 8 × 8 × 8 = 1072.76 c m 3

Height of cylinder=total height of vessel-radius of hemisphere
=15-8
=7cm
Volume of cylinder=

13 π r 2 h = 13 × 227 × 8 × 8 × 7 = 469.33 c m 3

Total volume of vessel=

1072.76 + 469.33 = 1542.09 c m 3

Therefore the correct option is 1.

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