A tall cylindrical container 6 cm in diameter contains some water. 9 steel spheres of diameter 4 cm are put into the water. If the all the spheres are under water and no water overflows from the container then the rise in water level is.
+128408 Note that the added volume of the spheres =
(9)(4/3)pi * (radius of the spheres)^3 =
(9)(4/3)pi * (2cm)^3 =
96pi cm^3 (1)
So.......the added volume can be considered as a new "cylinder" with a radius of 3 cm....and we have
Vcylinder = pi * r^2 * h .......subbing for the radius and setting this equal to (1), we have
96 pi cm^3 = pi * (3 cm)^2 * h
96 cm^3 = 9cm^2 * h divide both sides by 9 cm^2
(96/9)cm = h = 32/3 cm
So......the water rises 32/3 cm ≈ 10.666... cm
