Mensuration Practice Test 3

Question : 39 of 40

Marks: +1, -0

A sphere and a hemisphere have the same surface area. The ratio of their volumes is:

Solution:

Area of sphere = Area of hemisphere

4πR^2

3πr^2

4/3 R^2

r^2

r =

{2R}/√3

Ratio of the volumes of sphere and hemisphere
=

{4πR^3}/3 : {2πr^2}/3

2R^3 : r^3

2R^3 :({2R}/√3)^3

2R^3

{8R^3}/{3√3}

1 : 4/{3√3}

{3√3}/4 : 1

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