Worksheet: Surface Area of a Solid of Revolution

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 𝑦=36𝑥, 1𝑥1, is an arc of the circle 𝑥+𝑦=36. Find the area of the surface obtained by rotating this arc about the 𝑥-axis.

  • A12𝜋
  • B6𝜋
  • C24𝜋
  • D12
  • E24

Q2:

The arc of the parabola 𝑦=𝑥 from (1,1) to (2,4) is rotated about the 𝑦-axis. Find the area of the resulting surface.

  • A13171755
  • B𝜋3171755
  • C𝜋12171755
  • D16171755
  • E𝜋6171755

Q3:

Find the area of the surface generated by rotating the curve 𝑓(𝑥)=𝑥 over the interval [0,1] about the 𝑥-axis. Approximate your answer to the nearest one decimal place.

Q4:

Find the area of the surface generated by rotating the curve 𝑦=𝑒, where 0𝑥1, about the 𝑥-axis. Approximate your answer to the nearest one decimal place.

Q5:

Find the area of the surface generated by rotating the region bounded by 𝑥=1+2𝑦, 𝑥=0, 𝑦=1, and 𝑦=1 around the 𝑦-axis. Approximate your answer to the nearest one decimal place.

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