Answer:
The area of 3 slices is [tex]\frac{75}{8}\pi\ in^2[/tex] or approximate [tex]29.4\ in^2[/tex]
Step-by-step explanation:
Find out the area of the cookie cake
The area of the circle (cookie cake) is
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter
substitute
[tex]A=\pi (5)^{2}[/tex]
[tex]A=25\pi\ in^{2}[/tex]
Remember that the area of the complete cookie cake subtends a central angle of 360 degrees
If the cake is divided into 8 slices
then
The central angle of each slice is equal to
360/8=45°
The central angle of 3 slices is equal to
3(45°)=135°
By proportion
Find out the area of 3 slices
Let
x ----> the area of 3 slices
[tex]\frac{25\pi}{360}=\frac{x}{135}\\\\x=25\pi(135)/360\\\\x=\frac{3,375}{360}\pi\ in^2[/tex]
Simplify
[tex]\frac{75}{8}\pi\ in^2[/tex] ----> exact value of the area of 3 slices
Find out the approximate value of the area of 3 slices
assume
[tex]\pi =3.14[/tex]
substitute
[tex]\frac{75}{8}(3.14)=29.4\ in^2[/tex]
