# 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.