the ratio of surface area of a sphere and curved surface area of a hemisphere is 9:2 find ratio of their volumes
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Answer:
the ratio of surface area of a sphere and curved surface area of a hemisphere is 9:2 Then ratio of their volumes = 27:4
Step-by-step explanation:
surface area of a sphere = 4πR₁²
curved surface area of a hemisphere = 2πR₂²
surface area of a sphere/curved surface area of a hemisphere = 4πR₁²/2πR₂²
= 2R₁²/R₂²
2R₁²/R₂² = 9/2
=> R₁²/R₂² = 9/4
=> R₁²/R₂² = 3²/2²
=> R₁/R₂ = 3/2
Volume of sphere = (4/3)πR₁³
Volume of Hemisphere = (2/3)πR₂³
Volume of sphere /Volume of Hemisphere = ((4/3)πR₁³)/((2/3)πR₂³)
= 2 (R₁/R₂)³
= 2 (3/2)³
= 27/4
Ratio of their volumes = 27:4
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