Lesson Worksheet: Surface Area of a Solid of Revolution Mathematics
In this worksheet, we will practice applying definite integration to find the surface area of a solid generated by revolution of a region around an axis.
Q1:
The curve , , is an arc of the circle . Find the area of the surface obtained by rotating this arc about the .
- A
- B
- C
- D12
- E24
Q2:
The arc of the parabola from to is rotated about the . Find the area of the resulting surface.
- A
- B
- C
- D
- E
Q3:
Find the area of the surface generated by rotating the curve over the interval about the . Approximate your answer to the nearest one decimal place.
Q4:
Find the area of the surface generated by rotating the curve , where , about the . Approximate your answer to the nearest one decimal place.
Q5:
Find the area of the surface generated by rotating the region bounded by , , , and around the . Approximate your answer to the nearest one decimal place.
Q6:
Find the area of the surface obtained by revolving the curve , , about the line . Approximate your answer to three decimal places.
Q7:
When evaluating the surface area of the revolution of the arc defined by or , and , about the , which of the following rules is not true?
- A
- B
- C
- D
- E
Q8:
Consider the arc defined by the equation , .
Find the area of the surface obtained by rotating this arc about . Approximate your answer to four decimal places.
Q9:
Consider the arc defined by the equation , followed by the horizontal line .
Find the area of the surface obtained by rotating this arc about the . Approximate your answer to four decimal places.
Q10:
Find the area of the surface obtained by revolving the curve , , about the . Approximate your answer to three decimal places.
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