Question:
The height of a cone is 21 cm and its slant height is 28 cm. The volume of the cone is
(a) 7356 cm3
(b) 7546 cm3
(c) 7506 cm3
(d) 7564 cm3
Solution:
(b) $7546 \mathrm{~cm}^{3}$
Radius of the cone, $r=\sqrt{l^{2}-h^{2}}$
$=\sqrt{28^{2}-21^{2}}$
$=\sqrt{784-441}$
$=\sqrt{343} \mathrm{~cm}$
$\therefore$ Volume of the cone $=\frac{1}{3} \pi r^{2} h$
$=\frac{1}{3} \times \frac{22}{7} \times 343 \times 21$
$=22 \times 343$
$=7546 \mathrm{~cm}^{3}$
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