CBSE Class 10 Maths (Basic) 2024 · Paper 430(B)/S · Question 19

Surface Areas and Volumes 1 mark Hard

Assertion (A): If surface areas of two spheres are in the ratio

16 : 9

, then their volumes are in the ratio

64 : 27

. Reason (R): If

S_{1}

and

S_{2}

are the surface areas of two spheres and

V_{1}

and

V_{2}

are their volumes respectively, then

\frac{V _{1}}{V _{2}} = (\frac{S _{1}}{S _{2}})^{3/2}

Assertion (A): If surface areas of two spheres are in the ratio $16 : 9$ , then their volumes are in the ratio $64 : 27$ .

Reason (R): If $S_{1}$ and $S_{2}$ are the surface areas of two spheres and $V_{1}$ and $V_{2}$ are their volumes respectively, then $\frac{V _{1}}{V _{2}} = (\frac{S _{1}}{S _{2}})^{3/2}$ .

(a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c)Assertion (A) is true, but Reason (R) is false.
(d)Assertion (A) is false, but Reason (R) is true.

Answer

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

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CBSE Class 10 Maths (Basic) 2024 · Paper 430(B)/S · Question 19

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