The radius and the height of a right circular cone are in the ratio of 7 : 24 and its volume is 1232 cm3. Find the total surface area of the cone. (Use π = 22)
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 704 cm2.
Let the radius and height of the cone be 7x and 24x respectively.
Volume of cone = (1/3)πr2h
⇒ 1232 = (1/3) × (22/7) × 49x2 × 24x
⇒ x3 = 1
⇒ x = 1
Now, radius of cone = 7 cm, height of cone = 24 cm and slant height = 25 cm
Now, total surface area = πr(r + l)
⇒ (22/7) × 7(7 + 25)
⇒ 22 × 32 = 704 cm2