SOLUTION: A rectangular tin with base measuring 9cm by 7cm internally contains water to a depth of 4cm. An iron cylindrical bar 8cm long and 6cm in diameter is placed in the tin so that a ci

Algebra ->  Volume -> SOLUTION: A rectangular tin with base measuring 9cm by 7cm internally contains water to a depth of 4cm. An iron cylindrical bar 8cm long and 6cm in diameter is placed in the tin so that a ci      Log On


   

Question 1205079: A rectangular tin with base measuring 9cm by 7cm internally contains water to a depth of 4cm. An iron cylindrical bar 8cm long and 6cm in diameter is placed in the tin so that a circular face is in contact with the base. How far does the water level rise?
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Floor area = length*width
= 9*7
= 63 cm^2

Volume of water = (floor area)*height
= 63*4
= 252 cm^3

Or we could say it like this
Volume of water = length*width*height
= 9*7*4
= 252 cm^3

When placing the cylinder onto its circular end, the floor area will shrink.
It goes from 63 cm^2 to (63-9pi) cm^2
The 9pi is the area of the circle of radius 3 cm (i.e. diameter 6 cm).

h = new height

The old volume of water (252) will not change. This assumes the water doesn't spill of course.

old volume = 252
new volume = (new floor area)*(new height)
new volume = (63-9pi)*(h)
new volume = 252

(63-9pi)*(h) = 252
h = 252/(63-9pi)
h = 7.25688023221569
I used my calculator's stored version of pi to get the best accuracy possible.

If we rounded to let's say 4 decimal places, then the height is roughly h = 7.2569 cm