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 $\pi = 3.14$.

AcademicMathematicsNCERTClass 10

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.

raja
Updated on 10-Oct-2022 13:25:34

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