Core Pure 1 Chapter 5: Volumes of Revolution

4 flashcards · Mathematics · by TheoTyson

1. What is the volume of revolution when y = f (x)(x)(x) is rotated 2 π\piπ radians about the xxx -axis when x=ax=ax=a and x=bx=bx=b .

   π∫aby2 dx\pi \displaystyle \int_{a}^{b} y^2 \, dxπ∫ab​y2dx

2. What is the volume of revolution when x = f (y)(y)(y) is rotated 2 π\piπ radians about the yyy -axis when y=ay=ay=a and y=by=by=b .

   π∫abx2 dy\pi \displaystyle \int_{a}^{b} x^2 \, dyπ∫ab​x2dy

3. What is the formula for volume of a cylinder?

   πr2h\pi r^2hπr2h

4. What is the formula for volume of a cone?

   13πr2h\frac{1}{3} \pi r^2 h31​πr2h