Question
Download Solution PDFThe curved surface area of a right circular cone is 5400π cm2, and the diameter of its base is 144 cm. Find the height (in cm) of the cone.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Curved surface area (CSA) = 5400π cm2
Diameter of the base = 144 cm
Radius (r) = Diameter ÷ 2 = 144 ÷ 2 = 72 cm
Formula used:
CSA = π × r × l
l = slant height
l = √(r2 + h2)
Calculation:
5400π = π × 72 × l
⇒ l = 5400 ÷ 72
⇒ l = 75 cm
l = √(r2 + h2)
⇒ 75 = √(722 + h2)
⇒ 752 = 722 + h2
⇒ 5625 = 5184 + h2
⇒ h2 = 5625 - 5184
⇒ h2 = 441
⇒ h = √441
⇒ h = 21 cm
∴ The correct answer is option (2).
Last updated on Jul 22, 2025
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