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Question

A spherical glass vessel has a cylindrical neck 8cm long, 2cm in diameter; the diameter of the spherical part is 8.5cm.. By measuring the amount of water it holds, a child finds its volume to be 345cm3. Check whether she is correct, taking the above as the inside measurements, and π=3.14.


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Solution

Given

For the cylinder part, Height (h)=8cm and Radius (R)=22cm=1cm

For the spherical part, Radius (r)=8.52=4.25cm

Find out

We have to verify whether the measurements taken by the child are accurate

Amount of water it can hold = Total Volume of this vessel

= Volume of cylinder +Volume of a sphere

=πr2h+43πR3

=8π+102.35π

On considering π=3.14

=110.35π

=346.499cm3

Volume measured by child =345cm3,, which is not right

Correct volume =346.5cm3

Hence, the Correct volume=346.5cm3


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