Hello, jaswinder!

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 0.164 m².

Formulate and solve the simultaneous equations showing the relationship

between the external radius, R, and the internal radius, r, of the pipe.

They're mixing millimeters and meters . . . beware!

. . 0.164 m² = 164,000 mm²

The difference of radii is 75: .R - r .= .75 . → . r .= .R - 75 .[1]

The cross-sectional area is: .πR² - πr² .= .164,000 .[2]

Substitute [1] into [2]: .πR² - (R - 75)² .= .164,000

. . and we have: .150πR .= .5625π + 164,000

. . . . . . . . . . . . .5625p + 164,000

Therefore: . R .= .-------------------- .≈ .385.5 mm

. . . . . . . . . . . . . . . . 150p

. . . . and: . r .= .310.5 mm