Thread: Simpson's method

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!

Originally Posted by jaswinder

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!

What do you mean by "stible" method?

Originally Posted by ticbol

What do you mean by "stible" method?

It's a typo he meant to write: "using a suitable method".

RonL

Originally Posted by jaswinder

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