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.

Answer 1

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.