Respuesta :
Explanation
To solve this problem, we consider the area of a circular region with angle θ and radius r:
[tex]A(r,\theta)=\pi r^2\times\frac{\theta}{360\degree}.[/tex]From the statement, we know that we have two pizzas:
1) The small pizza has:
• a diameter and a radius:
[tex]d_s=10\text{ in}\rightarrow r_s=\frac{d_s}{2}=\frac{10\text{ in}}{2}=5\text{ in,}[/tex]• each of the six equal slices has an angle:
[tex]φ_s=\frac{360\degree}{6}=60\degree.[/tex]2) The large pizza has:
• a diameter and a radius:
[tex]d_l=18\text{ in}\rightarrow r_l=\frac{d_l}{2}=\frac{18\text{ in}}{2}=9\text{ in,}[/tex]• each of the two equal slices has an angle:
[tex]φ_l=\frac{360\degree}{12}=30\degree.[/tex](1) If Charles ate 5 slices of the large pizza, he ate an angle θ = 5*φl = 5*30° = 150°. Using the formula from above, we find that the area eaten by Charles is:
[tex]A(r_l=9\text{ in},\theta=150\degree)=\pi(9\text{ in})^2\cdot\frac{150\degree}{360\degree}\cong106.03\text{ in}^2.[/tex](2) If Julie ate 7 slices of the big pizza, she ate an angle θ = 7*φs = 7*60° = 420°. Using the formula from above, we find that the area eaten by Charles is:
[tex]A(r_s=5\text{ in},\theta=420\degree)=\pi(5\text{ in})^2\cdot\frac{420\degree}{360\degree}\cong91.63\text{ in}^2.[/tex]We have found that Charles ate an area of 106.03 in² and Julie an area of 91.63 in². We conclude that Charles ate more pizza than Julie.
AnswerCharles ate most pizza in terms of area.
