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Q.

The volumes of two hemispheres are in the ratio 27: 125. What is the ratio of the radii?


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a

2:7

b

3:5

c

7:9

d

1:3 

answer is B.

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Detailed Solution

Given- volumes of two hemispheres are in the ratio 27: 125.
Volume of hemisphere = 2 3 π r 3  
Let r 1   be the radius of first hemisphere and r 2   be the radius of second hemisphere.
   ⇒ 2 3 π r 1 3 2 3 π r 2 3 = 27 125 ⇒ r 1 3 r 2 3 = 27 125 ⇒ r 1 3 r 2 3 = 3 5 3 ⇒ r 1 r 2 = 3 5  
Thus, the ratio of the radii is 3:5.
Hence, option 2 is the correct option.
 
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The volumes of two hemispheres are in the ratio 27: 125. What is the ratio of the radii?