Two spheres are cut from a certain uniform rock. One has radius 4.50m. 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 r.
The volume of a sphere is given by the formula V = (4/3)πr^3.
Since the rock is uniform, the ratio of the volumes of the two spheres is equal to the ratio of their masses:
(4/3)π(4.50)^3 / (4/3)πr^3 = 1/5
Now we can solve for r:
(4.50)^3 / r^3 = 1/5
r^3 = (4.50)^3 * 5
r = (4.50) * 5^(1/3)
r ≈ 7.09m
Therefore, the radius of the second sphere is approximately 7.09m.