A culvert is constructed out of large cylindrical shells cast in concrete, as shown in the figure. The volume of the cylindrical shell is 
.
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Factor this to show that 
.
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Use the ''unrolled'' diagram to explain why this makes sense geometrically.
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What will be an ideal response?
The volume of the cylindrical shell equals the volume of parallepiped shown in the figure. The length of parallepiped is 
. The thickness is 
and the height is h so .You might also like to view...
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction.F = 4yi + 8xj + z3k; C: the counterclockwise path around the perimeter of the triangle in the x-y plane formed from the x-axis, y-axis , and the line y = 3 - 6x
A. 1 B. - 6 C. 3 D. 6
Solve the percent of change problem.In a local election, 32,600 people voted. This was a decrease of 7% over the last election. How many people voted in the last election? Round to the nearest whole number when necessary.
A. 30,467 people B. 34,882 people C. 35,054 people D. 30,318 people
Solve the problem.Bobby built a house of cards 17 ft 1 in. tall. Pam built a house of cards 
tall. How much taller is Bobby's house of cards than Pam's?
A. 3 ft 2 in. B. 3 ft 1 in. C. 3 ft 11 in. D. 4 ft 12 in.
Solve the mixture problem.How many liters of a 10% alcohol solution must be mixed with 90 liters of a 50% solution to get a 20% solution?
A. 36 liters B. 360 liters C. 270 liters D. 27 liters