The radius of the base of a right circular cone is 7 cm and its curved surface area is 550 cm2. Find the volume of the cone. (Use π = 22/7)
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Correct answer: D
Explanation
The correct answer is Option 4 i.e. 1232 cm3.
The volume of the cone = 1/3πr2h and,
The curved surface of the cone = πrl [l = slant height]
⇒ 550 = πrl
⇒ 550 = 22/7 × 7 × l
⇒ l = 25
Slant height = l2 = h2 + r2
⇒ 252 = h2 + 72
⇒ 625 - 49 = h2
⇒ h2 = √576
⇒ h = 24 cm
Now,
The volume of the cone = 1/3πr2h = 1/3 × 22/7 × 7 × 7 × 24 = 1232 cm3