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Question
Assertion (A)
If the volumes of two spheres are in the ratio 27 : 8, then their surface areas are in the ratio 3 : 2.
Reason (R)
Volume of a sphere `=4/3pi"R"^3`
Surface area of a sphere = 4πR2
Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).- Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
- Assertion (A) is true and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
Solution
Assertion (A) is false and Reason (R) is true.
Assertion (A):
Let R and r be the radii of the two spheres.
Then, ratio of their volumes `=(4/3pi"R"^3)/(4/3 pi"r"^3)`
Therefore,
`=(4/3pi"R"^3)/(4/3 pi"r"^3) = 27/8`
`⇒ "R"^3/"r"^3 = 27/8`
`=> ("R"/"r")^3 = (3/2)^3`
`=> "R"/"r" = 3/2`
Hence, the ratio of their surface areas`= (4 pi"R"^2)/(4pi"r"^2)`
`="R"^2/"r"^2`
`=("R"/"r")^2`
`=(3/2)^2`
`=9/4`
= 9 : 4
Hence, Assertion (A) is false.
Reason (R): The given statement is true.
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