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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 |
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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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