Q. 795.0( 1 Vote )

Assertion (A): If the volumes of two sphere are in the ratio 27:8 then their surface areas are in the ratio 3:2

Reason (R): Volume of a sphere .

Surface area of a sphere = 4πR

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.

Answer :

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: πr^{3}

Let V_{1} be the volume of the first sphere.

Let V_{2} be the volume of the first sphere.

∴ V_{1}:V_{2} = π(r_{1})^{3} : π(r_{2})^{3}

⇒ 27:8 = (r_{1})^{3} : (r_{2})^{3}

⇒ r_{1} : r_{2} = 3:2

Surface area of the sphere is given by: 4πr^{2}

Let S_{1} be the Surface area of the sphere.

Let S_{2} be the Surface area of the sphere.

∴ S_{1} : S_{2} = 4π(r_{1})^{2}:4π(r_{2})^{2}

⇒ S_{1} : S_{2} = (r_{1})^{2}: (r_{2})^{2}

⇒S_{1} : S_{2} = (3)^{2}: (2)^{2}

⇒S_{1} : S_{2} = 9:4

Reason(R):

Volume of a sphere = πr^{3}.

Surface area of a sphere = 4πR^{2}.

Assertion is wrong and Reason is Wrong.

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