Question

A 10 inch cookie cake is divided into 8 slices. What is the area of 3 slices

Answer 1

Answer:

The area of 3 slices is $\frac{75}{8}\pi\ in^2$  or approximate $29.4\ in^2$

Step-by-step explanation:

Find out the area of the cookie cake

The area of the circle (cookie cake) is

$A=\pi r^{2}$

we have

$r=10/2=5\ in$ ----> the radius is half the diameter

substitute

$A=\pi (5)^{2}$

$A=25\pi\ in^{2}$

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

$\frac{25\pi}{360}=\frac{x}{135}\\\\x=25\pi(135)/360\\\\x=\frac{3,375}{360}\pi\ in^2$

Simplify

$\frac{75}{8}\pi\ in^2$ ----> exact value of the area of 3 slices

Find out the approximate value of the area of 3 slices

assume

$\pi =3.14$

substitute

$\frac{75}{8}(3.14)=29.4\ in^2$