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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.
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 $102.66\ cm^3$.
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