Question

Byron’s house has a roof with dimensions shown. (Roof: 1m Height, 7m Hypotenuses, 12m length)

He knows that the average rainfall in his
suburb is 30cm per year. Byron would like
to install a cylindrical rainwater tank to hold the
water that runs off the roof. The tank is to be made of
moulded plastic but Byron wants to minimise the
area of moulded plastic required and hence the cost.

Can you help Byron answer the following questions?
1) What volume of water will fall on the roof per year?
2) How many litres of water does the tank need to hold?
3) How high will a tank that has base diameter 3 m need to be?
4) What is the surface area of moulded plastic required to build the tank in 3?
5) Suggest the dimensions of the tank so that the minimum amount of moulded plastic
is used.

Answer 1

the volume of water hitting the roof is just the area of the roof's horizontal projection, times the depth of the rainfall.
That is just 12√48 * .30 m^3 = 24.94m^3

1 m^3 = 1000L, so the barrel needs to hold 24900L.

v = πr^2h, so π(3/2)^2h = 24.94
h = 3.53m

I expect you can take it from here, eh?