Question

A sphere and a cube have the same surface area. Find out the ratio of the volume of the

sphere to that of the cube.

Answer 1

Given, Surface area of sphere = surface area of cube

             4pir^2 = 6x^2

               r^2/x^2 = 6/4pi

               r/x = root 3/2pi


 The volume of the sphere = 4/3 pir^3 and volume of the cube = x^3.

4/3pir^3/x^3

= (4pi/3)(r/x)^3

= (4pi/3)(3/2pi)^1.5

= root 2 * root 3/root pi

= root 6/root pi.

Ratio = root 6 : root pi


Hope this helps!

Answer 2

hello users .......

given that 
sphere and a cube have the same surface area

we have to find out 
the ratio of the volume of the sphere to that of the cube

solution :-
we know that 
volume of cube = a³  ( where a is the side of cube )

and 
volume of  sphere = 4πr³ / 3

and 
surface area of cube = 6 a²
and 
surface area of sphere = 4πr²

now 
according to question 
 6 a² = 4πr²

now 
ratio of volumes = volume of sphere / volume of cube 
=           $\frac{4 \pi r^{3} }{3 * a^{3} }$
  =              $\frac{4 \pi r^{2} * r }{3 a^{3} }$

=          $\frac{6 * a^{2} * r }{3 a^{3} }$ 

=             $\frac{2 r }{a}$

hence

they are in ratio of 2r : a 

where r is radius of sphere and a is side of cube 

⊕⊕ hope it helps ⊕⊕