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Volumes: Integrating Cross-sections- HW Problems
1. Find the volume of the solid whose base is the disk in the 𝑥-𝑦 plane
bounded by 𝑥 2 + 𝑦 2 = 9 and whose cross sections when sliced by a
plane perpendicular to the 𝑥-axis are
a. squares
b. semicircles
c. equilateral triangles.
2. find the volume of the solid whose base is the region in the 𝑥-𝑦
plane bounded by 𝑦 = 4 − 𝑥 2 and the 𝑥-axis and whose cross sections
when sliced by a plane perpendicular to the 𝑦-axis are
a. squares
b. isosceles right triangles with the hypotenuse in the base.
Find the volume of the solid obtained by rotating the region bounded
by the curves below about the given line.
3. 𝑦 = 1 − 𝑥, 𝑥 = 0, 𝑦 = 0, about the 𝑥-axis
4. 𝑦 = 𝑥 2 , 𝑦 = 4, 𝑥 = 0, about the 𝑥-axis
5. 𝑦 = 𝑥 2 , 𝑦 = 0, 𝑥 = 2, about the 𝑦-axis
6. 𝑦 = 𝑒 𝑥 , 𝑥 = 0, 𝑥 = 1, 𝑦 = 0, about the 𝑥-axis
7. 𝑦 = 𝑥 2 , 𝑦 = √𝑥 , about the line 𝑦 = −2
8. 𝑦 = 𝑥 2 , 𝑦 = √𝑥, about the line 𝑥 = −1
Volumes: Integrating Cross-sections- HW Problems
1. Find the volume of the solid whose base is the disk in the 𝑥-𝑦 plane
bounded by 𝑥 2 + 𝑦 2 = 9 and whose cross sections when sliced by a
plane perpendicular to the 𝑥-axis are
a. squares
b. semicircles
c. equilateral triangles.
2. find the volume of the solid whose base is the region in the 𝑥-𝑦
plane bounded by 𝑦 = 4 − 𝑥 2 and the 𝑥-axis and whose cross sections
when sliced by a plane perpendicular to the 𝑦-axis are
a. squares
b. isosceles right triangles with the hypotenuse in the base.
Find the volume of the solid obtained by rotating the region bounded
by the curves below about the given line.
3. 𝑦 = 1 − 𝑥, 𝑥 = 0, 𝑦 = 0, about the 𝑥-axis
4. 𝑦 = 𝑥 2 , 𝑦 = 4, 𝑥 = 0, about the 𝑥-axis
5. 𝑦 = 𝑥 2 , 𝑦 = 0, 𝑥 = 2, about the 𝑦-axis
6. 𝑦 = 𝑒 𝑥 , 𝑥 = 0, 𝑥 = 1, 𝑦 = 0, about the 𝑥-axis
7. 𝑦 = 𝑥 2 , 𝑦 = √𝑥 , about the line 𝑦 = −2
8. 𝑦 = 𝑥 2 , 𝑦 = √𝑥, about the line 𝑥 = −1
