Question:
The volume of hemisphere is equal to the volume of cylinder. Calculate the ratio of total surface area of hemisphere and total surface area of cylinder. The radius of hemisphere and cylinder is equal.
The volume of hemisphere is equal to the volume of cylinder. Calculate the ratio of total surface area of hemisphere and total surface area of cylinder. The radius of hemisphere and cylinder is equal.
Updated On: Jul 8, 2025
- 4: 7
- 6: 11
- 9: 10
- 3: 5
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The Correct Option is C
Solution and Explanation
The correct option is (C): 9:10.
Let the radius of hemisphere = r unit
Radius of hemisphere = radius of cylinder = r unit
Height of cylinder = h unit
Volume of sphere = volume of cylinder
(\(\frac{2}{3}\)) * π*r3 = π*r2 *h
(\(\frac{2}{3}\)) *r = h
r = (\(\frac{3h}{2}\))
Ratio of total surface area of hemisphere and total surface area of
cylinder
=\( \frac{(3*π*r2) }{ [2*π*r (r + h)]}\)
=\( \frac{(3 *r) }{{2[r + (\frac{2r}{3})]}}\)
= \(\frac{(3*r) }{ [2 (\frac{5r}{3})]}\)
= \(\frac{9 }{10}\)
= 9:10.
Let the radius of hemisphere = r unit
Radius of hemisphere = radius of cylinder = r unit
Height of cylinder = h unit
Volume of sphere = volume of cylinder
(\(\frac{2}{3}\)) * π*r3 = π*r2 *h
(\(\frac{2}{3}\)) *r = h
r = (\(\frac{3h}{2}\))
Ratio of total surface area of hemisphere and total surface area of
cylinder
=\( \frac{(3*π*r2) }{ [2*π*r (r + h)]}\)
=\( \frac{(3 *r) }{{2[r + (\frac{2r}{3})]}}\)
= \(\frac{(3*r) }{ [2 (\frac{5r}{3})]}\)
= \(\frac{9 }{10}\)
= 9:10.
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