1
Area of a Surface of Revolution- HW Problems
Find the surface area of the surface obtained by rotating the curve
about the 𝑥-axis.
1. 𝑦 = 2√𝑥 ; 1≤𝑥≤4
𝜋
2. 𝑦 = cos(𝑥 ) ; 0≤𝑥≤
2
3. 𝑥 = 1 + 2𝑦 2 ; 1≤𝑦≤2
𝑥3 1
4. 𝑦 =
6
+ 2𝑥 ; 1≤𝑥≤2
1 3
5. 𝑥 = (𝑦 2 + 2)2 ; 0≤𝑦≤2
3
Find the surface area of the surface obtained by rotating the curve
about the 𝑦-axis.
6. 𝑦 = 4 − 𝑥 2 ; 0≤𝑥≤2
3
7. 𝑦 = √𝑥 ; 1≤𝑥≤8
1 1
8. 𝑦 = 𝑥 2 − ln(𝑥 ) ; 1≤𝑥≤2
4 2
9. 𝑥 = √𝑎2 − 𝑦 2 ; 0≤𝑦≤𝑎
Area of a Surface of Revolution- HW Problems
Find the surface area of the surface obtained by rotating the curve
about the 𝑥-axis.
1. 𝑦 = 2√𝑥 ; 1≤𝑥≤4
𝜋
2. 𝑦 = cos(𝑥 ) ; 0≤𝑥≤
2
3. 𝑥 = 1 + 2𝑦 2 ; 1≤𝑦≤2
𝑥3 1
4. 𝑦 =
6
+ 2𝑥 ; 1≤𝑥≤2
1 3
5. 𝑥 = (𝑦 2 + 2)2 ; 0≤𝑦≤2
3
Find the surface area of the surface obtained by rotating the curve
about the 𝑦-axis.
6. 𝑦 = 4 − 𝑥 2 ; 0≤𝑥≤2
3
7. 𝑦 = √𝑥 ; 1≤𝑥≤8
1 1
8. 𝑦 = 𝑥 2 − ln(𝑥 ) ; 1≤𝑥≤2
4 2
9. 𝑥 = √𝑎2 − 𝑦 2 ; 0≤𝑦≤𝑎
