Question

How to solve for the amount of square inches of pizza eaten

Answer 1

Answer:

Jeremy ate 31.4 square inches of pizza

Step-by-step explanation:

Given:

A circle divided into 8 portions with 5 out of the total shaded representing the amount ate

To find:

The amount of square inches Jeremy ate

Each of the divided parts represents a sector of a circle. So, to find the amount ate, we need to calculate the area of sector

First, we need to get the angle for each sector

Total angles in a circle = 360°

The circle was divided into 8

The angle in each portion = 360/8

The angle in each portion = 45°

The formula for the area of sector of a circle:

`Area\text{ }of\text{ }a\text{ }sector=(θ)/(360)×πr²`

substitute the values into the formula:

`\begin{gathered} Area\text{ of the sector = }(45)/(360)*\text{ 3.14}*4^2 \\ \\ Area\text{ of the sector = 6.28 in}^2 \end{gathered}`

This means each of the sector as an area of 6.26 square inches

5 slices were eaten. So the area for the 5 slices = 5 × area of each sector

`\begin{gathered} Total\text{ area for the 5 slices = 5 }*\text{ 6.28} \\ Total\text{ area for the 5 slices = 31.4in}^2 \end{gathered}`

Hence, Jeremy ate 31.4 square inches of pizza