A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular .ends are 4 cm and 2 cm. Find the capacity of the glass.

AcademicMathematicsNCERTClass 10

Given:

A drinking glass is in the shape of a frustum of a cone of a height of 14 cm. The diameters of its two circular ends are 4 cm and 2 cm.

To do:

We have to find the capacity of the glass.

Solution:

Upper diameter of the frustum $= 4\ cm$

This implies,

Upper radius $r_1 = \frac{4}{2}$

$= 30\ cm$

Lower diameter of the frustum $= 2\ cm$

This implies,

Lower radius $r_2 = \frac{2}{2}$

$= 1\ cm$

Height of the frustum(glass) $h = 14\ cm$

Therefore,

Volume of the frustum $=\frac{\pi}{3}[r_{1}^{2}+r_{1} r_{2}+r_{2}^{2}] \times h$

$=\frac{\pi}{3}[(2)^{2}+2 \times 1+(1)^{2}] \times 14$

$=\frac{14\pi}{3}[4+2+1]$

$=\frac{14\times22}{7\times3} \times 7$

$=102.66 \mathrm{cm}^{3}$

The capacity of the glass is $102.66\ cm^3$.

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

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