MATH 2411 #4: QUESTION 3



#3: 4a) ANSWER : You get a slanted ring which is a segment of a cone

#3: 4b) ANSWER: .
SOLUTION:
If the ring segment is very narrow, then the formula for the surface area is where r is the average radius of the ring and t is the width of the ring.

#3: 4c) ANSWER:
SOLUTION: In this case r is the distance the segment is from the x-axis which is y = x 2 and t is the arc length of the segment. Therefore,

#3: 4d) ANSWER:

#3: 4e) ANSWER:

#3: 4f) ANSWER: .
SOLUTION: In this case, r is the distance the segment is from the y-axis which is x and t is the arc length of the segment. Therefore,

#3: 4g) ANSWER: