Question

the amount of glass needed to create a cylindrical vase that has the surface area s, is $s = 2pi r^2 + 2pi rh$. express the surface area in factored form.

Explanation:

Step1: Identify common factor

The expression is \( S = 2\pi r^2 + 2\pi rh \). The common factor in both terms is \( 2\pi r \).

Step2: Factor out the common factor

Using the distributive property \( ab + ac = a(b + c) \), we factor out \( 2\pi r \) from \( 2\pi r^2 + 2\pi rh \).
\( S = 2\pi r(r + h) \)

Answer:

\( S = 2\pi r(r + h) \)