Question

The TSA of a sphere and a cube is same.Show that the ratio of the volume of the cube to that of the sphere is √pi:√6.

Answer 1

We know, Tsa of sphere =4pi r^2 Tea of cube = 6a^2 Given tsa s are equal ⇒4pi r^2=6a² ⇒4/6 π r² = a² Curbing on both sides we get 64/216 π³ r^6 =a^6. ...............(1) Now, Vol. of sphere= 4/3 π r³ Vol. of cube= a³ So to find ratio we div. both , ⇒4/3 π r³ whole div by a³ Let's square the eq. As we know the value of a^6 ⇒ 16/9 π² r^6 whole div. by a^6. By sub . In here we get , 16/9²πr^6 whole div by 64/216 π ³ r^6 After cancellation we get, 6/π Remember we squared the ratio! So now we sq. root to get back the real ratio, We get √6/√π We get here the Ratio of vol. of sphere to vol. of cube..... Hence proved..... Hope it helps ... Scratched my brain so much. ☺️ Any doubt u can ask....