Respuesta :
Given:
a) The radius is doubled.
b) The radius is tripled.
To find:
The changes to the surface area of a sphere
Explanation:
Let us take the original radius as r.
The surface area of the original sphere is,
[tex]A=4\pi r^2[/tex]a) The new radius will be,
[tex]R=2r[/tex]So, the surface area of the sphere with the new radius is,
[tex]\begin{gathered} A=4\pi R^2 \\ =4\pi(2r)^2 \\ =4\pi(4r^2) \\ A=4(4\pi r^2) \\ A=4\times Surface\text{ area of old sphere} \end{gathered}[/tex]Therefore, the surface area of a sphere becomes four times the original surface area if the radius is doubled.
b) The new radius will be,
[tex]R=3r[/tex]So, the surface area of the sphere with the new radius is,
[tex]\begin{gathered} A=4\pi R^2 \\ =4\pi(3r)^2 \\ =4\pi(9r^2) \\ A=9(4\pi r^2) \\ A=9\times Surface\text{ area of old sphere} \end{gathered}[/tex]Therefore, the surface area of a sphere becomes nine times the original surface area if the radius is tripled.
