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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 $\pi = 3.14$.
Given:
A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter, and 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 $345\ cm^3$.
To do:
We have to check whether the child is correct or not.
Solution:
The volume of water the glass vessel can hold $= 345\ cm^3$
Radius of the cylindrical part $= \frac{2}{2}$
$= 1\ cm$
Height of the cylindrical part $= 8\ cm$
Therefore,
The volume of the cylindrical part $= \pi r^2h$
$= 3.14 \times (1)^2 \times 8$
Diameter of the spherical part $=8.5\ cm$
This implies,
Radius $= \frac{8.5}{2}$
$= \frac{85}{20}$
$=\frac{17}{4}\ cm$
Therefore,
Volume of the spherical part $=\frac{4}{3} \pi r^{3}$
$=\frac{4}{3} \times 3.14 \times \frac{17 \times 17 \times 17}{4 \times 4 \times 4}$
$=321.39 \mathrm{~cm}^{3}$
The total volume of the glass vessel $=$ Volume of the cylindrical part $+$ Volume of the spherical part
$= 25.12 + 321.39$
$= 346.51\ cm^3$
Volume measured by the child is $345\ cm^3$ which although close is not exactly correct.
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