Q. 795.0( 1 Vote )

# Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:Assertion (A): If the volumes of two sphere are in the ratio 27:8 then their surface areas are in the ratio 3:2Reason (R): Volume of a sphere .Surface area of a sphere = 4πR2.A. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).B. Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).C. Assertion (A) is true and Reason (R) is false.D. Assertion (A) is false and Reason (R) is true.

Assertion is wrong and Reason is Wrong.

Explanation:

Assertion (A):

Given: volumes of two sphere are in the ratio 27:8.

Volume of the sphere is given by: πr3

Let V1 be the volume of the first sphere.

Let V2 be the volume of the first sphere.

V1:V2 = π(r1)3 : π(r2)3

27:8 = (r1)3 : (r2)3

r1 : r2 = 3:2

Surface area of the sphere is given by: 4πr2

Let S1 be the Surface area of the sphere.

Let S2 be the Surface area of the sphere.

S1 : S2 = 4π(r1)2:4π(r2)2

S1 : S2 = (r1)2: (r2)2

S1 : S2 = (3)2: (2)2

S1 : S2 = 9:4

Reason(R):

Volume of a sphere = πr3.

Surface area of a sphere = 4πR2.

Assertion is wrong and Reason is Wrong.

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