6.6mm of rain fall onto a rectangular roof 8m long and 6m wide. The rain water drains into a cylindrical barrel of diameter 60cm. How far does the water level rise in the barrel
Depth of rain = D = 0.66 cm
Width of rain = W = 600 cm
Length of rain = L = 800 cm
Volume of rain = V = D*W*L = 0.66*600*800 = 316,800 cc
Let H be the height of the water level (in cm) in the barrel.
Volume of water in barrel is Vb = pi*R^2 * H (and R = 30 cm)
Vb = pi*(30)^2* H = 2,827.4H cc
And Vb = 316,800 cc (volume of water drained from roof)
So, 316,800 = 2,827.4H
H = 316,800/2,827.4
H = 112 cm