Volumes of Solids of Revolution – AP Calculus AB | ShowMeClass

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Volumes of Solids of Revolution

AP Calculus AB · Unit 8: Applications of Integration

Learning Objectives

Compute volumes using the disk/washer method

Compute volumes using the shell method

Visualize revolution around x-axis and y-axis

Approximate volume with finite slices (Riemann disks)

Disk/Washer Method

Shell Method

Visual Guide

f(x) — outer radius

g(x) — inner radius (washer)

Revolution region

Disk/shell slices

VolumeRevolutionDisk/WasherShellAP Calc AB

Method—

Axis—

V (exact)—

V (approx)—

2D CROSS-SECTION

Function f(x)

Method

Revolve Around

Lower Bound a 0.00

Upper Bound b 2.00

Number of Slices n 10

3D Rotation Angle 45°

Volume Calculation

📝 Quick Quiz▼

1. The volume of y=√x revolved around the x-axis from 0 to 4 is:

4π 8π 16π 2π

2. The washer method is used when:

The region is above the axis There's a hole in the cross-section f(x) is negative Revolving around y-axis only

3. Shell method integrates:

π[R(x)]² dx 2πx·f(x) dx πx² dy 2πy dy