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

1. 
   Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
3. Assertion (A) is true and Reason (R) is false.
4. Assertion (A) is false and Reason (R) is true.

Answer 1

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.