Question
Download Solution PDFThe curved surface area of a right circular cone is 20π cm2 . If its radius is 4 cm, then find the volume of cone.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Curved surface area (CSA) of the cone = 20π cm2
Radius (r) = 4 cm
Formula Used:
Curved surface area (CSA) = π × r × l
Volume of the cone = (1/3) × π × r2 × h
where l is the slant height and h is the height of the cone.
Calculation:
From the CSA formula:
20π = π × 4 × l
⇒ 20 = 4 × l
⇒ l = 5 cm
Using Pythagoras' theorem in the cone:
l2 = r2 + h2
⇒ 52 = 42 + h2
⇒ 25 = 16 + h2
⇒ h2 = 25 - 16
⇒ h2 = 9
⇒ h = 3 cm
Volume of the cone:
Volume = (1/3) × π × 42 × 3
⇒ Volume = (1/3) × π × 16 × 3
⇒ Volume = 16π cm3
The correct answer is 16π cm3
Last updated on Jun 26, 2025
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