# 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.