If the radius of the base of a cone be 7 cm and its curved surface area be 550 sq. cm, then the volume of the cone is? यदि एक शंकु के आधार की त्रिज्या 7 सेमी. हो और उसका वक्र पृष्ठीय क्षेत्रफल 550 वर्ग सेमी. हो तो, शंकु का आयतन कितना होगा?
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1132 sq.cm/वर्ग सेमी.
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1324 sq.cm/वर्ग सेमी.
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1232 sq.cm/वर्ग सेमी.
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1024 sq.cm/वर्ग सेमी.
C
Correct answer
Explanation
Curved surface area of cone = πrl = 550 cm². With r = 7 cm: π × 7 × l = 550, so l = 550/(7π) = 25 cm. Using Pythagorean theorem: h = √(l² - r²) = √(625 - 49) = √576 = 24 cm. Volume = (1/3)πr²h = (1/3) × π × 49 × 24 = 392π = 1232 cm³. Note: options incorrectly show sq.cm instead of cu.cm.