The volume of a right circular cone of height 24 cm is 1232 cm3.

Question:

The volume of a right circular cone of height 24 cm is 1232 cm3. Its curved surface area is
(a)  1254 cm2
(b) 704 cm2
(c) 550 cm2
(d) 462 cm2

Solution:

(c) 550 cm2
Let r cm be the radius of the cone.
Volume of the right circular cone  = 1232 cm3
Then we have:

$\frac{1}{3} \times \frac{22}{7} \times r^{2} \times 24=1232$

$\Rightarrow r^{2}=\frac{1232 \times 21}{22 \times 24}$

$\Rightarrow r^{2}=49$

$\Rightarrow r=7 \mathrm{~cm}$

$\therefore$ Curved surface area of the cone $=\pi r l$

$=\frac{22}{7} \times 7 \times \sqrt{7^{2}+24^{2}}$

$=22 \times \sqrt{49+576}$

$=22 \times 25$

$=550 \mathrm{~cm}^{2}$

 

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