15 My Notes Ask Yur A culvert is constructed out of large cy

15. My Notes Ask Yur A culvert is constructed out of large cylindrical shells cast in concrete, as shown in the figure. Using the formula for the volume of a cylinder given on the inside back cover of this book, explain why the volume of the cylindrical shell is Factor to show that -2x-average radius . height . thickness. Since average radius height h, and thickness ,we see the following 2 2x average radius height thickness Use the \"unrolled\" diagram to explain why this makes sense geometrically. Since th, \"unrolled-diagram is a rectangular shell, V-height-thickness-length. From the diagram, we see the following height length (average circumference of the cylindrical shell) Thus, the formula of the cylindrical shell makes sense geometrically Need Help? Ehiniu

Solution

V = 2 • Averagee radius • height • thickness

Average radius = (R+r)/2 , thicknss = R-r

V = R²h - r²h

= 2h(R²-r²)/2

= 2h(R-r)(R+r)/2

= 2 • (R+r)/2 • h • (R-r)

Now,

Unrolled diagram in rectangular shell

V = height • thickness • length

Height = h

Thickness = R-r

Length = (2R+2r)/2 = (R+r)