The height of a cone is 21 cm and its slant height is 28 cm.
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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