Question

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

Answer 1

The area of 3 slices is
`(75)/(8)\pi\ in^2` or approximate
`29.4\ in^2`

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

`(25\pi)/(360)=(x)/(135)\\\\x=25\pi(135)/360\\\\x=(3,375)/(360)\pi\ in^2`

Simplify

`(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

`(75)/(8)(3.14)=29.4\ in^2`