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प्रश्न
No Question.
उत्तर
Radius of the bigger sphere = r cm
Radius of smaller spheres = r1 cm
\[\frac{\text { Volume of bigger sphere }}{\text { Volume of small spheres }} = \frac{\frac{4}{3} \pi r^3}{\frac{4}{3}\pi r_1^3} = \frac{r^3}{r_1^3} = 8\]
\[ \Rightarrow \left( \frac{r}{r_1} \right)^3 = \left( \frac{2}{1} \right)^3 \]
\[ \Rightarrow \left( \frac{r}{r_1} \right) = \left( \frac{2}{1} \right)\]
Hence, r : r1 = 2 : 1.
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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.
