Two solid spheres A and B are made from the same material. The mass of sphere B is eight times that of sphere A. If the radius of sphere A is 7.50 cm, what is the radius of sphere B? [Volume of a sphere of radius r is given by V = 4ðr63/3]

15cm

To solve this problem, we can use the fact that the volume of a sphere is proportional to the cube of its radius.

Let's denote the radius of sphere B as Rb. We know that the mass of sphere B is eight times that of sphere A. Since both spheres are made of the same material, the ratio of their masses is equal to the ratio of their volumes.

The volume of sphere A is given by Va = (4/3)π(r^3), where r is the radius of sphere A.

Similarly, the volume of sphere B is given by Vb = (4/3)π(Rb^3), where Rb is the radius of sphere B.

We can write the ratio of their volumes as:

Va/Vb = (4/3)π(r^3) / (4/3)π(Rb^3)

Since the (4/3)π terms cancel out, we have:

Va/Vb = r^3 / Rb^3

Given that the mass of sphere B is eight times that of sphere A, we can write:

Va/Vb = 1/8

Substituting the values, we get:

r^3 / Rb^3 = 1/8

To solve for Rb, we can take the cube root of both sides:

(Rb^3)^(1/3) = (r^3)^(1/3) / (1/8)^(1/3)

Simplifying further:

Rb = r / (1/2)

Given that the radius of sphere A is 7.50 cm, we substitute r = 7.50 cm into the equation:

Rb = 7.50 cm / (1/2)

Rb = 7.50 cm * 2

Rb = 15 cm

Therefore, the radius of sphere B is 15 cm.