Question

Find the area of a circle whose area equals the half of the sum of the areas of two circles with radii 2 and 3.

can someone help me im working on Circles: Area of Circles and like i never worked on this kinda of stuff

Answer 1

So what is the area of a circle with radius 2:
A = pir^2 = pi*(2)^2=4pi

Answer 2

A=pir^2=pi*(3)^2=9pi thats the area of the circle with radius 3

Answer 3

Sum of the areas is:
4pi+9pi = 13pi
half that sum is 13pi/2

Answer 4

So A = 13pi/2

Answer 5

\[A=\pi*r^2\]

\[A=\frac{1}{2}[\pi*2^2+\pi*3^3]=\frac{1}{2}[4 \pi+ 9 \pi]=\frac{1}{2}13\pi=\frac{13\pi}{2}\]