The base area of a cone is 7546 cm2 and the area of the curved surface is 7854 cm2. The height (in cm) of the cone is : (Use π = 22/7)
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Correct answer: D
Explanation
The correct answer is option 4 i.e 10 .
Base area = 7546 cm²
Curved surface area = 7854 cm²
Use π = 22/7
Base area = π × r²
⇒ 7546 = (22/7) × r² ⇒ r² = (7546 × 7) ÷ 22 = 2401 ⇒ r = √2401 = 49 cm
CSA = π × r × l
⇒ 7854 = (22/7) × 49 × l ⇒ (22/7) × 49 = 154 ⇒ 7854 = 154 × l ⇒ l = 7854 ÷ 154 = 51 cm
l² = r² + h² ⇒ 51² = 49² + h²
⇒ 2601 = 2401 + h² ⇒ h² = 200
h = √200 = 10 cm