Jeremy ate 31.4 square inches of pizza
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:
[tex]Area\text{ }of\text{ }a\text{ }sector=\frac{θ}{360}×πr²[/tex][tex]\begin{gathered} θ=\text{ 45\degree} \\ diameter\text{ = 8 inches} \\ diameter\text{ = 2\lparen radius\rparen} \\ radius\text{ = diameter/2} \\ radius\text{ = 8/2 = 4 inches} \\ let\text{ \pi = 3.14} \end{gathered}[/tex]substitute the values into the formula:
[tex]\begin{gathered} Area\text{ of the sector = }\frac{45}{360}\times\text{ 3.14}\times4^2 \\ \\ Area\text{ of the sector = 6.28 in}^2 \end{gathered}[/tex]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
[tex]\begin{gathered} Total\text{ area for the 5 slices = 5 }\times\text{ 6.28} \\ Total\text{ area for the 5 slices = 31.4in}^2 \end{gathered}[/tex]Hence, Jeremy ate 31.4 square inches of pizza
