Thread: cylinder

A cylindrical concrete sewer pipe is to be cast so that the concrete is uniformly 75mm thick while the cross section of the concrete is 0.164m^2.
formulate and solve the simultaneous equations showing the relationship between the external radius R and the internal radius r of the pipe.

Originally Posted by zak_killcity14@hotmail.co

A cylindrical concrete sewer pipe is to be cast so that the concrete is uniformly 75mm thick while the cross section of the concrete is 0.164m^2.
formulate and solve the simultaneous equations showing the relationship between the external radius R and the internal radius r of the pipe.

The cross-sectional area is simply the area of the circle of external radius R with the area of the circle of internal radius r subtracted. So:
0.164 = (pi)(R^2 - r^2)

We also know that
0.075 = R - r

Thus: R = 0.075 + r

Inserting this into the first equation:
0.164 = (pi)([0.075 + r]^2 - r^2)

0.164 = (pi)(0.150r + 0.005625)

Which you can solve for r. Then you can use that value of r in the R = 0.075 + r equation to get R.

I get r = 0.311 m and R = 0.386 m (or so.)

-Dan