Chapter 4.6, Problem 127ES

Volume of Carpeting. The volume of a carpet that is rolled up can be estimated by the polynomial $\pi R^{2}h-\pi r^{2}h$, where R and r represent the radii of two circles, as shown in the following figure.

a. Factor the polynomial.

b. Use both the original form and the factored form to find the volume of a roll for which

$R=50\text{ cm},r=10\text{ cm and }h=4\text{ m}$. Use 3.14 for $\pi$.