The curved surface area of a right circular cone is 20π cm2 . If its radius is 4 cm, then find the volume of cone.  

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SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 10 Jul, 2024 Shift 2)
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  1. 20 π cm3
  2. 16 π cm3
  3. 18 π cm3
  4. 21 π cm3

Answer (Detailed Solution Below)

Option 2 : 16 π cm3
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Detailed Solution

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Given:

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

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