Question

Which equation represents the area of one base of a cylinder if the radius is doubled?

Answer 1

Answer:

If the radius is doubled, then the area of one base of a cylinder  quadrupled and the equation is:

$\boxed{A_{b1}=4\pi r^2}$

Explanation:

The surface area of a solid is the total area of its outer surface. For a cylinder whose radius of its circular base is $r$, and height $h$, then the surface area (S) can be calculated as:

$S=\text{Surface area of base 1}+\text{Surface area of base 2}+\text{Surface area of the side} \\ \\ S=A_{b1}+A_{b2}+A{s} \\ \\ S=\pi r^{2}+\pi r^{2}+2\pi rh \\ \\ S=2\pi r^{2}+2\pi rh \\ \\ \\ Because: \\ \\ \text{Surface area of base 1}=\text{Surface area of base 2} \\ \\ \\ Where: \\ \\ A_{b1}:\text{Surface area of base 1} \\ \\ A_{b2}:\text{Surface area of base 2} \\ \\ A_{s}:\text{Surface area of the side}$

So, if the radius is doubled then the area of one base is:

$A_{b1}=\pi (2r)^{2} \\ \\ A_{b1}=\pi (4r^2) \\ \\ \boxed{A_{b1}=4\pi r^2}$