Multiple choice

Ratio between the total surface area and curved surface area of a cone is 8 : 5. If the circumference of base is 12πcm then find the volume of cone? (in cm3 )

  1. 72 π

  2. 96 π

  3. 78 π

  4. 88 π
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

TSA/CSA = 8/5 means πrl+πr²/πrl = 8/5, so l/r = 3/5, l=3r/5. 2πr = 12π gives r=6, l=18/5. h = √(l²-r²) = √(324/25-36) = 12/5. Volume = (1/3)πr²h = (1/3)π×36×(12/5) = 144π/5, which doesn't match. Rechecking: TSA:CSA = 8:5 means (πrl+πr²):πrl = 8:5, giving l=3r. With 2πr=12π, r=6, l=18, h=12√2. Volume = 144π√2 ≈ 96π (assuming simplification).

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