If a right circular cone of height 24 cm has a volume of 1232 cm³, then what is the total surface area of the cone? (Use π = 22/7)

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Accepted Answer

Let the radius of the base be r cm and the height h = 24 cm. The volume of a cone is given by V = (1/3)πr²h. Given V = 1232 cm³ and π = 22/7:

(1/3) × (22/7) × r² × 24 = 1232
=> (22/7) × r² × 8 = 1232
=> (22/7) × r² = 1232 / 8 = 154
=> (22/7) × r² = 154
=> r² = 154 × (7/22) = 49
=> r = √49 = 7 cm

Now, slant height l = √(r² + h²) = √(7² + 24²) = √(49 + 576) = √625 = 25 cm

Total surface area of cone = πr(l + r)
= (22/7) × 7 × (25 + 7)
= 22 × 32
= 704 cm²

Therefore, the total surface area is 704 cm².

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