If the ratio of the volumes of the two sphere is 125 64 find the ratio of their surface areas...

Question

If the ratio of the volumes of the two sphere is 125 64 find the ratio of their surface areas

Accepted Answer

Solution The amount of space that a sphere can occupy is measured by its volume If we take a circular disc attach a string to its circumference then rotate it along the string we can create a circle on a piece of paper This provides us a spherelike form Given ratio of volume of two spheres 12564 43 rsub1subsup3sup43 rsub2subsup3sup 12564 rsub1subsup3sup rsub2subsup3sup 12564 Taking cube root on both sides rsub1subrsub2sub 54 Ratio of surface areas of the spheres 4 rsub1subsup2sup4 rsub2subsup2sup rsub1subsup2suprsub2subsup2sup 5sup2sup4sup2sup 2516 Hence the ratio of the surface areas is 2516

ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.3 in Chapter 17 - Mensuration