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The radii of two solid spheres are 10 cm and 20 cm. The ratio between their volumes is :

  1. 3 : 8

  2. 1 : 4

  3. 1 : 8

  4. 8 : 3

The radii of two solid spheres are 10 cm and 20 cm. The ratio between their volumes is : Cylinder, Cone, Sphere, Concise Mathematics Solutions ICSE Class 10.

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Answer

Radius of first solid sphere (r) = 10 cm

Radius of second solid sphere (R) = 20 cm

Ratio of volumes of two spheres :

⇒Vol. of 1st sphereVol. of 2nd sphere=43πr343πR3=r3R3=103203=10008000=18=1:8.\Rightarrow \dfrac{\text{Vol. of 1st sphere}}{\text{Vol. of 2nd sphere}} = \dfrac{\dfrac{4}{3}πr^3}{\dfrac{4}{3}πR^3} \\[1em] = \dfrac{r^3}{R^3} \\[1em] = \dfrac{10^3}{20^3} \\[1em] = \dfrac{1000}{8000} \\[1em] = \dfrac{1}{8} \\[1em] = 1 : 8.

Hence, Option 3 is the correct option.

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