If the combined area of the white and orange regions is 100π, what is the area of only the orange region? a) 16π b) 36π c) 64π d) 96π

Answers

We know the combined area is 100π, and the combined area includes the white section as well as the orange section.

now, if we take the area of the white circle, and "subtract" it from the combined area, we're in effect, making a whole in the larger circle, and what's leftover is just the orange part, because the white would have been subtracted out,

\bf \textit{area of a white circle}\\\\
A=\pi r^2\quad 
\begin{cases}
r=radius\\
-----\\
r=6
\end{cases}\implies A=\pi 6^2\implies A=36\pi 
\\\\\\
\stackrel{combined~area}{100\pi }~~-~~\stackrel{white~circle's~area}{36\pi }\implies \stackrel{orange~section}{64\pi }
The area of orange=total-white

given
all=100pi

remember
area=pi times radius^2
white radius is 6
area=pi6^2
area=36pi

areaorange=areatotal-areawhite
areaorange=100pi-36pi
areaorange=64pi square units
64π is correct, since the area of the white circle is 36π, and 100π - 36π = 64π.
64π is the answer.
100\pi-36\pi=64π
64π is the answer.
100\pi-36\pi=64π
Using the picture above. If the area area of the combined regions is 100pi, you have to subtract the center region which has a radius of 6.
100pi - 64 pi leaves an area of 64pi.   LETTER C
The image is here, i am struggled  with this problems too please help!
If the combined area of the white and orange regions is 100π, what is the area of only the orange re


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