A culvert is constructed out of large cylindrical shells cast in concrete, as shown in the figure. Using the formula for the vol
ume of a cylinder given on the inside back cover of this book, explain why the volume of the cylindrical shell is V = πR2h − πr2h. Factor to show that V = 2π · average radius · height · thickness Since average radius = Incorrect: Your answer is incorrect. , height = h, and thickness = Incorrect: Your answer is incorrect. , we see the following. V = πR2h − πr2h = 2πh 2 = 2πh(R − r) 2 = 2π · 2 · h · R − r = 2π · average radius · height
1 answer:
A cylindrical shell has a hollow part that is found inside a cylinder. Because the inside part is hollow, you don't account that as part of the total volume. If you look at the picture attached, the hollow part is the red area. We only account for the yellow area because that is the volume of concrete. Hence, the volume is difference of the outer volume to the inner volume.
Volume of Cylindrical Shell = Volume of Outside cylinder - Volume of inside cylinder
Since the volume of a cylinder is πr²h,
Volume of Cylindrical Shell = πR²h - πr²h
Volume of Cylindrical Shell = Volume of Outside cylinder - Volume of inside cylinder
Since the volume of a cylinder is πr²h,
Volume of Cylindrical Shell = πR²h - πr²h
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Answer:
∠EGB and ∠AGF are congruent;
Transitive Property of Equality
Step-by-step explanation:
The vertical angles theorem is about the angles that are opposite to each other. These angles are formed when two lines cross each other
Vertical angles are congruent i.e their measures are equal
Look at the attached graph
Given:
AB // CD
E , G , H , F are col-linear
The line which contains points E , G , H , F is a transversal for the parallel lines AB and CD
∵ AB and EF intersected at point G
∴ m∠EGB = m∠AGF ⇒ by the vertical angles theorem
When lines AB and EF intersected at G they formed opposite angles like angles EGB and AGF, then angles EGB and AGF are congruent ( vertical angle theorem)
∵ AB // CD and EF is a transversal
∴ m∠AGF = m∠CHF (corresponding angles theorem)
Transitive Property of Equality: if one angle is equal to two other angles, then the two other angles are equal
Therefore, If a = b and b = c, then a = c
∵ m∠EGB = m∠AGF
∵ m∠AGF = m∠CHF
∴ m∠EGB = m∠CHF (transitive property theorem)
∠EGB and ∠AGF are congruent; Transitive Property of Equality
