A small cone of base area 9 Πcm2 and volume of 12Πcm3 is cut from a larger cone of base area 25Πcm2 and volume 75 Πcm3 then find the height of the remaining solid?

Base area ratio 9:25 means radius ratio is 3:5. Volume ratio 12:75. Volume = (1/3)πr²h, so h ratio = volume ratio / (radius ratio)². h₁/h₂ = (12/75) / (9/25) = (12/75) × (25/9) = (4/25) × (25/9) = 4/9. So small cone has height 4 units. If large cone height is 5 units, remaining solid height = 5 - 4 = 1? Wait, let me recalculate: V ∝ r²h, so h ∝ V/r². Small: 12/9 = 4/3. Large: 75/25 = 3. Ratio 4:3 : 3 = 4:9. So if large cone h = 5, small cone h = 20/9 ≈ 2.22. Remaining = 5 - 2.22 ≈ 2.78. This doesn't match options. Actually using the ratio directly: h₁/h₂ = (V₁/V₂) × (r₂²/r₁²) = (12/75) × (25/9) = 4/9. If heights are in ratio 4:9 and volumes are 12π and 75π, let's say h₁ = 4x, h₂ = 9x. But volumes suggest h₁ = 4, h₂ = 9 (in ratio units). Option C says remaining = 5, which would mean large - small = 9 - 4 = 5.