a water tower is 24m high and circular in plan. The inside radii ofthe tower at different heights are given in the follow table:
Height(metres) 0 6 12 18 24
Radii(metres) 10 8 7 6 6.5
Using a stible method find the capacity of the tower in cubic metres.
working out showing too would be greatly appreciated!
By a suitable method I will assume that Simpsons rule is required.
V = integral pi r^2 dh, h=0..24
Simpson's rule tells us that:
integral f(x) dx a,b ~= h/3 [f(x0) + 4*f(x1) + 2*f(x2) + ... + 4*f(x(n-1)) +f(xn)]
where h=(b-a)/n.
So here we have h=6, n=4, and so:
V ~= 2 [(pi 10^2) + 4*(pi 8^2) + 2*(pi 7^2) + 4*(pi 6^2) +(pi 6.5^2)] ~= 4022.8 cubic metres.
RonL