Question : The volume of a right circular cone is 1232 cm3 and its vertical height is 24 cm. Its curved surface area is:
Option 1: 154 cm2
Option 2: 550 cm2
Option 3: 604 cm2
Option 4: 704 cm2
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Correct Answer: 550 cm 2
Solution : Given: The volume of a right circular cone is 1232 cm 3 and its vertical height is 24 cm. Let $r$, $h$, and $l$ be the radius, height, and slant height of the cone. According to the question, $\frac{1}{3}×\pi×r^2×h=1232$ Or, $\frac{1}{3}×\frac{22}{7}×r^2×24=1232$ Or, $r^2=\frac{1232×7×3}{22×24}$ Or, $r^2=49$ Or, $r=7$ cm. Now, $l^2=h^2+r^2$ Or, $l^2=24^2+7^2$ Or, $l^2=576+49$ Or, $l=\sqrt{625}=25$ cm. Therefore, its curved surface area = $\pi×r×l$ = $\frac{22}{7}×7×25$ = 550 cm 2 . Hence, the correct answer is 550 cm 2 .
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