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

Question

Mensuration at O level

Answer 1

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