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A drinking glass is shaped like a frustum of a cone with a height of 14 cm. The diameters of its two circular ends are 4 cm and 2 cm, respectively. Determine the volume of the glass.

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92.67 cubic cm

115.21 cubic cm

102.67 cubic cm

80.21 cubic cm

answer is A.

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Detailed Solution

Given:

$h = 14 cm, r_{1} = \frac{4}{2} = 2 cm and r_{2} = \frac{2}{2} = 1 cm$

The volume of the frustum of a cone

$= \frac{1}{3} π h (r_{1}^{2} + r_{2}^{2} + r_{1} r_{2})$

$= \frac{1}{3} \times \frac{22}{7} \times 14 (2^{2} + 1^{2} + 2 \times 1)$

$= \frac{44}{3} (4 + 1 + 2)$

$= \frac{44 \times 7}{3}$

$= \frac{308}{3} = 102.67$ cubic cm

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