5.2 Volumes of Solids (Disk, and Washer Methods)

Area of a semi circle- $A=\frac12\pi r^2$

Area of a circle- $A=\pi r^2$

Volume equations:

Cylinder- $V=Ah$

Circular cylinder- $V=\pi r^2h$

Rectangular box- $V=lwh$

Sphere- $V=\frac43\pi r^3$

Disk Method

To find the volume of a solid when the cross section is…

perpendicular to the x axis = in terms of x: $V=\int_{a}^{b}A\left(x\right)\!\,dx$

perpendicular to the y axis = in terms of y: $V=\int_{c}^{d}\!A\left(y\right)\,dy$

Washer Method

$V=\int_{a}^{b}\!A\left(x\right)\,dx$

$A\left(x\right)=A\left\lbrack f\left(x\right)\right\rbrack-A\left\lbrack g\left(x\right)\right\rbrack$