1.

Find the area of curved surface of a right circular cone (in cm2) of height 24 cm, having volume 1232 cm3.1). 5502). 7043). 9244). 1254

Answer»

Formula: Volume of a right circular cone $(= \;\frac{{\pi {r^2}h}}{3})$

And area of curved SURFACE of right circular cone = πrl

Given: volume = 1232 cm3

Height = 24 cm

$(\therefore \frac{{\pi {r^2}h}}{3} = 1232)$

$(\Rightarrow \frac{{22}}{7} \times {r^2} \times \frac{{24}}{3} = 1232)$

$(\Rightarrow {r^2} = \frac{{1232 \times 7}}{{22 \times 8}} = 49)$

⇒ r = 7 cm

By Pythagoras theorem, $(L\; = \;\sqrt {{r^2} + {h^2}} )$

$(\therefore l\; = \sqrt {{7^2} + {{24}^2}} )$

l = 25 cm

Now, area of curved surface = π r l

$(\therefore Curved\;surface\;area = \frac{{22}}{7} \times 7 \times 25 = 550\;c{m^2})$


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