What it the relation betweet small ball with large ball?

Question

Into a regular glass tank, 8 small steel balls are placed. Then the tank is filled with water so that the top of the water is level with the very top of the 8 steel balls.

The 8 balls are removed and replaced with 1 larger Steel Ball (into the same tank with the same water, none is lost).

The larger Steel Ball is submerged in the water to exactly half of its diameter.

Which is true:

a.) The larger steel ball is exactly twice the diameter of the smaller ones.

b.) The diameter of the larger steel ball is less than twice the diameter of the smaller ones.

c.) The diameter of the larger steel ball is greater than twice that of the smaller ones.

d.) Cannot be determined.

Volume of Sphere = 4/3( Pi) r3

Pi = 3.141592653589793 (approx

Answer 1

First assume that the smaller steel balls have a radius of 1ft (units are not important because everything is relative) also for simplicity assume Pi =3.14. So Pi*4/3*1^3 = 4.19 and there are 8 balls so, 4.19*8 = 33.5 ft cubed. We also know the large ball displaces the same amount of water when half of its volume is submerged so 33.5 = 0.5*Pi*4/3*r^3

r^3 = 33.5/(0.5*Pi*4/3) = 16ft cubed.

Take the cube root and find r. r is greater than three (I do not have a calculator so I do not have the exact numerical answer), we know that the radius is half the diameter so if the diameter is 2 for the smaller balls it is greater than 6 for the larger balls therefore the answer C, more than twice the diameter of the smaller balls