# Simpson's method

• Feb 22nd 2007, 11:57 AM
jaswinder
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!
• Feb 24th 2007, 08:16 PM
ticbol
Quote:

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?
• Feb 24th 2007, 10:34 PM
CaptainBlack
Quote:

Originally Posted by ticbol
What do you mean by "stible" method?

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

RonL
• Feb 24th 2007, 10:47 PM
CaptainBlack
Quote:

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