Question
The radius and height of a right circular cone are in
the ratio 3: 4. If its curved surface area (in cm²) is 240 π, then its volume (in cm³) is:Solution
Curved surface area of cone = π r l Volume of cone = (1/3) π r2 h Slant height = √(h2 + r2 ) Let the radius and height of the cone be 3x and 4x Slant height = √[(4x)2 + (3x)2 ] ⇒ √(16x2 + 9x2 ) ⇒ √25x ⇒ 5x Curved suface area = π × 3x × 5x2 ⇒ 240 π = π × 15x ⇒ x2 = 16 ⇒ x = 4 Radius = 12 cm Height = 16 cm Slant height = 20 cm Volume of the cone = (1/3) × π × 144 × 16 ⇒ 48 × 16 × π ⇒ 768 π
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