top button
Flag Notify
    Connect to us
      Site Registration

Site Registration

A cylinder of dia 4cm is filled with water & 300 lead balls increases its level by .8 cm. What is the dia of each ball?

+1 vote
460 views

A cylindrical vessel of diameter 4cm is partly filled with water and 300 lead balls are dropped into it which increases its level by .8 cm. What is the diameter of each ball?

posted Mar 2, 2016 by anonymous

Share this puzzle
Facebook Share Button Twitter Share Button LinkedIn Share Button

2 Answers

0 votes

Diameter of each ball is 8.6mm.
First find the volume of the water rise. V = 3.14 x r x r x h. V = 3.14 x 2 x 2 x 8 = 100.53. This is then equal to the volume of 300 lead balls.
Now Volume of a ball (sphere) is: V = 4/3 x 3.14 x r x r x r, so for 300 balls, 100.53 = 300*4/3*3.14*r*r*r. If you work this out, the answer comes to 4.3mm. As the question asks for diameter, then the final answer is 8.6mm.

answer Mar 2, 2016 by Ben Tangatakno
its .8 cm not 8, do you like to correct your answer (use edit button)
I can fix it.
Volume increase = pi * R^2 * h
Volume of all balls = N * 4/3 * pi * r^3
Both volumes equal:
pi * R^2 * h = N * 4/3 * pi * r^3
h = N * 4/3 * r^3/R^2
r^3 = 3/4 * h/N *R^2 = (2*d)^3
d = 0.5 * (3/4 * 0.8/300 * 4 * 4)^(-3)
d = 0.5 * (0.8 * 4/100)^(-3)
d = 0.5 * 0.032^(-3) (exact answer)
It gives a diameter of 1.59 mm per ball.
Still this diameter issue... sorry, replace R by 2cm:
d = 0.5 * (3/4 * 0.8 / 300 * 2 * 2)^(-3)
d = 0.5 * 0.008^(-3)
Thus the exact answer should rather be a diameter of 1 mm per ball.
0 votes

Volume of water rise
V1=Pi*R^2*h.......................(R is radius of cylinder=D/2=4/2=2cm=20mm)
V1=Pi*20*20*8...........................(all dimensions are in mm)
V1=3200Pi............................(i)
Volume of 300 sphere balls
V2=300*(4/3)*Pi*r^3
V2=400*Pi*r^3........................(ii)
as V1+V2 so
3200Pi=400Pir^3
3200=400r^3
r=2mm
d=4mm
Ans :Dia. of each ball is 4mm

answer Mar 2, 2016 by Jaikumar Bhatia



Similar Puzzles
+2 votes

When a conical bottle rests on its flat base, the water in the bottle is 8 cm from the cone's vertex, When the same conical bottle is turned upside down, the water surface is 2 cm from the flat base.

What is the height of the bottle?

enter image description here

0 votes

A coin of diameter 1 cm. is rolling on the periphery circle of diameter 24 cm, how many rounds will this coin need to revolve to complete one full big circumference?

0 votes

If each individual square has a side length of 4cm in the following figure, what is the perimeter of the cross?

Cross Perimeter

...