Question

A fish tank is 50 cm long, 34 cm wide and 24 cm high. It contains water to depth of 18 cm. Four identical spheres are placed in the tank and are fully submerged. The water level rises by 4.5 cm.

1.What is the volume before the spheres were added?
2. What is the volume of each sphere?
3. What is the radius of the spheres?

Answer 1

Archimedes would have done it this way

original volume
= 50x34x18
=30600

change in volume
= 50x34x4.5
= 7650
---- caused by the two spheres

so each sphere had a volume of 3825 cm^3

V of sphere = (4/3)πr^3
(4/3)πr^3 = 3825
r^3 = 913.151..
r = cuberoot(913.151...) = appr 9.70 cm