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.

Guest Apr 8, 2017

#1**+3 **

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

V_{cylinder} = 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

CPhill
Apr 8, 2017