The volume of the ball is the same as the volume of the prism, which has a volume of 48 cm3. Find the radius of the ball.

Given:

Vsh = Vp,

Vp = 48 cm ^ 3.

Find – R.

By determining the volume of the ball:

Vsh = 4/3 * n * R ^ 3.

From the formula for the volume of the sphere, we express the radius of the sphere:

4/3 * n * R ^ 3 = Vn;

4 * n * R ^ 3 = Vn * 3;

R ^ 3 = Vn * 3 / (4 * n);

R = ∛ (Vp * 3 / (4 * n)).

Substitute numerical values into the formula for the radius and find it:

R = ∛ (48 * 3 / (4 * 3)) = ∛12 = 2 (cm).

Answer: R = 2 cm.