the ratio of the volumes of two spheres is 27:64. if the sum of their radii is 56 cm; find the radius of the smaller sphere

Let's denote the radius of the smaller sphere as r1 and the radius of the larger sphere as r2. We know that the sum of their radii is 56 cm, so we can write the equation:

r1 + r2 = 56

We also know that the ratio of the volumes of the two spheres is 27:64. The volume of a sphere is given by the formula (4/3)πr^3, so we can write the equation:

(r1^3) / (r2^3) = 27 / 64

We can simplify this equation to:

r1 / r2 = cuberoot(27 / 64)

Now we have a system of two equations, and we can solve it step by step.

First, let's solve the second equation for r1:

r1 = r2 * cuberoot(27 / 64)

Now we can substitute this into the first equation:

r2 * cuberoot(27 / 64) + r2 = 56

We can simplify this to:

r2 * (cuberoot(27 / 64) + 1) = 56

Now we can solve for r2:

r2 = 56 / (cuberoot(27 / 64) + 1)

Once we have the value for r2, we can substitute it back into the equation r1 + r2 = 56 to find r1.