Volumes Of Revolution

Question 1

Parametric volumes of revolution

Answer 1

Square x or y depending on which axis
Multiply by dy/dt or dx/dt
Find limits in terms of y and integrate with respect to t
Multiply by pi

Question 2

Parametric volume about the x-axis

Answer 2

a
π ∫ y^2 dx/dt dt
b

a, b should be limits of t

Question 3

Parametric volume about the y-axis

Answer 3

a
π ∫ x^2 dy/dt dt
b

a, b should be limits of t