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What will be the capacity of a vessel, which is in the form of a hemispherical bowl surmounted by a hollow cylinder, having the diameter as 21 cm and the total height as 14.5 cm?

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3811.5 cm 3

3811 cm 3

3812.5 cm 3

3815.5 cm 3

answer is A.

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Detailed Solution

Given,
The vessel is having the diameter as 21 cm and the total height as 14.5 cm.
We have to find the capacity of the vessel.
Applying formula for radius:

(r) = diameter 2

∴ r = 212 ⇒ r = 10.5 cm

Applying the formula for volume of the hemisphere:
Volume of the hemisphere

= 23 π r 3

∴ Volume of the hemisphere = 23 × 227 × 10.5 × 10.5 × 10.5 ⇒ Volume of the hemisphere = 2425.5 cm 3

Note that, height of the cylinder=

total height of the vessel − radius of sphere

=14.5-10.5
=4 cm
Applying the formula for volume of the cylinder:
Volume of the cylinder

= π r 2 h

∴ Volume of the cylinder = 227 × 10.5 × 10.5 × 4 ⇒ Volume of the cylinder = 1386 cm 3

And, total volume = volume of cylinder + volume of hemispherical part.

∴ Total volume = 1386 + 2425.5 ⇒ Total volume = 3811.5 cm 3

So, the capacity is

3811.5 cm 3

Therefore, option 1 is correct.

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