Rainfall on a flat rectangular roof 10m by 5.5m flows into a cylindrical tub of a diameter 3m find in cm the increase in depth of the water in the tub caused by a rainfall of 1.2 cm help please?

Answer 1

This is a clever problem. It sounds really complicated, but that's only because
it's actually two simple problems rolled into one.

The two problems are:
1). Volume of a rectangular prism
2). Volume of a cylinder
Before we get started, let's make sure you remember the formulas for both of
those volumes:
1). Rectangular prism . . . V = (length) x (width) x (height)
2). Cylinder . . . Volume = (pi) x (radius)2 x (height)
The attack is:
-- Figure out the volume of the water that rained onto the roof.
-- Realize that the same volume poured into the cylindrical tub.
-- Figure out how deep that much water fills the cylinder.
At this point, the hard part is done! The problem is as good as solved.

-- 1.2 cm of rain falls on the 10m x 5.5m rectangular roof. How much water is sitting on the roof ?
Volume = L x W x H = (10m) x (5.5m) x (0.012 m) = 0.66 cubic meter of water
-- Now pour that water into the cylinder with 3m diameter. How deep is it ?
Volume = (pi) x (radius)2 x (height) .
We need to find the height, so solve this formula for the height.
Divide each side of equation by (pi) x (radius)2 :
Height = Volume / (pi) x (radius)2
The volume is the 0.66 m3 that poured off of the roof.
The radius is 1/2 of the diameter = 1.5m .
So Height = (0.66)/(pi) x (1.5)2 = 0.09337 meter = 9.337 cm.