If the volume of two spheres are in ratio 64:27. What is the ratio of their surface area
To find the ratio of the surface area of two spheres, we must first find the radius of each sphere.
Let the volumes of the two spheres be V1 and V2, and let the radii of the spheres be r1 and r2. Since the volume of a sphere is proportional to the cube of its radius, we have:
(V1/V2) = (r1^3 / r2^3) = 64/27
Taking the cube root of both sides, we get:
(r1/r2) = 4/3
Now, the surface area of a sphere is given by the formula A = 4πr^2. So, the ratio of the surface areas of the two spheres is:
(A1/A2) = (4πr1^2) / (4πr2^2) = (r1^2 / r2^2)
Substitute the ratio of radii we found earlier:
= ((3/4)^2) = 9/16
Therefore, the ratio of the surface areas of the two spheres is 9:16.