Question

A standard medium pizza has a diameter of 12 inches and is cut into 8 slices.
What is the area and what is the one sector area of a slice of pizza.

Please show work. I've been stuck on this for a while and want to understand it.

Answer 1

Answer:

The answer to your question is Circle's area = 113.04 in²  Slice' area = 14.13 in²

Step-by-step explanation:

Data

diameter = 12 in

8 slices

Area = ?

Area of a slice = ?

Process

1.- Calculate the area of the pizza

radius = 12/2

radius = 6 in

Area = πr²

-Substitution

Area = (3.14)(6)²

-Simplification

Area = 113.04 in²

2.- Calculate the area of the slice

We can calculate this area by two methods

a) Divide the area of the number of slices

       Area of the slice = 113.04 / 8

                                   = 14.13 in²

b) Using the area of a sector

-Find the angle of each slice

               360 / 8 = 45°

-Convert 45° to rad

                180° ------------------- πrad

                  45° ------------------- x

                  x = 45πrad/180

                  x = 1/4πrad

- Calculate the area of the sector

Area = 1/4(3.14)(6)²/2

Area = 113.04/8

Area = 14.13 in²                        

Answer 2

Answer:

Step-by-step explanation:

Assuming the pizza is circular, we would apply the formula for determining the area of a circle. It is expressed as

Area = πr²

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Diameter = 12 inches

Radius = 12/2 = 6 inches

Area = 3.14 × 6² = 113.04 inches²

The formula for determining the area of a sector is expressed as

Area of sector = θ/360 × πr²

Where θ represents the central angle.

The complete circle or pizza is 360°. Since it is divided into 8 equal parts, then the central angle formed by each sector is

360/8 = 45°

Therefore,

Area of sector = 45/360 × 3.14 × 6²

= 14.13 inches²