State the conservation principle

The total volume of the bowl (up to the brim) is equal to the sum of the volume of the water and the volume of the ball.

$V_{bowl} = V_{water} + V_{ball}$

Calculate the volume of the ball

Using the sphere volume formula with radius 2 cm:

$V_{ball} = \frac{4}{3} \pi (2)^3 = \frac{32\pi}{3}$

Sum the volumes

Total volume of the bowl = (992$\pi/3) + (32\pi/3) = 1024\pi/3$cm³.

$V_{bowl} = \frac{992\pi + 32\pi}{3} = \frac{1024\pi}{3}$

Solve for the radius of the bowl

Equating the total volume to the hemisphere volume formula: (2/3)$\pi R$³ = 1024$\pi/3.$Cancelling $\pi/3$gives 2R³ = 1024, so R³ = 512.

$R = \sqrt[3]{512} = 8$