Question

6.6millimeters of rain fall into a rectangular roof. 8meters long and 6 meters wide. The rainwater drains into a cylindrical barrel of diameter 60centimeters. How far does the water level rise in the barrel​

Answer 1

1.12 meters

Explanation:

this is the same as filing a box with the same ground area 6.6 millimeters high and then drain it at once into the barrel.

so, the volume of the box filling is (1 m = 1000 mm)

Vb = 8000 × 6000 × 6.6

now, this is then also the volume of the cylinder when filling it up with everything inside the box.

and the general volume of a cylinder is (as for the box) ground area times height.

just here the ground area is a circle with the diameter of 60 cm and therefore the radius of 60/2 = 30 cm.

1 cm = 10 mm => r = 300 mm

the area of a circle is

Ac = pi×r²

=>

Vc = pi×r²×h(eight) = pi×300²×h

and that is also the value of Vb.

Vc = Vb = pi×90000×h

h = Vb / (pi×90000) = 8000×6000×6.6/(pi×90000) =

= 800×6×6.6/(pi×9) = 800×2×2.2/pi = 800×4.4/pi =

= 1120.45 mm = 1.12 m