Two spheres are cut from a certain uniform rock. One has radius 4.50cm. The mass of the other is five times greater. Find its radius. Give your answer to 2 decimal places.
Let the radius of the second sphere be denoted by r.
The mass of a sphere is directly proportional to the cube of its radius. Therefore, the ratio of the masses of the two spheres is equal to the ratio of the cubes of their radii.
(5/1) = (r^3) / (4.5^3)
5 = r^3 / 91.125
r^3 = 5 * 91.125
r^3 = 455.625
Taking the cube root of both sides:
r = 7.32 cm
Therefore, the radius of the second sphere is 7.32 cm.