Chapter 12.3, Problem 40WE

To determine

To show: The volume of the solid formed is $\frac{1}{4}\pi s^3$

Answer to Problem 40WE

The volume of the solidformed is $\frac{1}{4}\pi s^3$ cu. units

Explanation of Solution

Given information: Consider the given information,

An equilateral triangle with sides of length s is rotated in space about one side.

Radius = $\frac{\sqrt{3}}{2}s$ units

Height = $\frac{s}{2}$ units

Formula used: Consider the given formula,

r = radius, h = height

Volume = $\frac{1}{3}\pi r^{2}h$

Calculation : Consider the given information the formula is,

Let ABC is a triangle , $OC=\frac{\sqrt{3}}{2}s$

Volume of the solid formed = $\frac{1}{4}\pi {(\frac{\sqrt{3}}{2}s)}^2\times s=\frac{\pi }{4}{s}^3$ cu. units