The inside of a bowl is part of a sphere. When water is put into the bowl to a depth d, the water surface becomes a circle of radius 2d. What is the radius of the sphere?

Given:

The inside of the bowl is part of a sphere.

Depth of water (d) = d

Radius of the water surface = 2d

Formula used:

Using the geometry of spheres, the radius of the sphere (R) is given by:

R = \(\frac{(r^2 + d^2)}{2d}\)

Where r = radius of the water surface = 2d

Calculation:

R = \(\frac{(r^2 + d^2)}{2d}\)

⇒ R = \(\frac{((2d)^2 + d^2)}{2d}\)

⇒ R = \(\frac{(4d^2 + d^2)}{2d}\)

⇒ R = \(\frac{5d^2}{2d}\)

⇒ R = 2.5d

∴ The correct answer is option (1).