The area of slice is 25.133 square inches and the length of its crust is 6.283 inches, if the pizza that has a diameter of 16 inches. If her slice has a central angle of 45º.
Step-by-step explanation:
The given is,
Diameter of pizza is 16 inches
If her slice has a central angle of 45º
Step:1
Ratio of slice to pizza if slice has a central angle of 45º ,
= [tex]\frac{45}{360}[/tex]
[tex]= \frac{1}{8}[/tex][tex]\frac{1}{8}[/tex]
Area of Pizza is, (pizza is a circular shape),
[tex]A = \pi r^{2}[/tex]..............................(1)
Where, r - Radius of pizza
From given,
Diameter, D = 16 inches
r = [tex]\frac{D}{2} = \frac{16}{2}[/tex]
r = 8 inches
Equation (1) becomes,
[tex]A = \pi 8^{2}[/tex]
[tex]= (3.14)(64)[/tex] (∵ [tex]\pi =3.1415[/tex] )
= 201.0619 square inches
Area of pizza slice,
= Ratio of slice to pizza × Area of pizza
= [tex](\frac{1}{8} )[/tex] × 201.0619
= 25.133 square inches
Area of pizza slice = 25.133 square inches
Step:2
Formula for perimeter of pizza,
[tex]P = 2\pi r[/tex]................................(2)
Where, r - Radius of pizza
From given, r = 8 inches
Equation (2) becomes,
[tex]= 2 (3.1415)(8)[/tex] (∵ [tex]\pi =3.1415[/tex] )
= 50.265 inches
Perimeter of slice is,
= Ratio of slice to pizza × Perimeter of pizza
= [tex](\frac{1}{8} )[/tex] × 50.265
= 6.283 inches
Length of crust (slice) = 6.283 inches
Result:
The area of slice is 25.133 square inches and the length of its crust is 6.283 inches, if the pizza that has a diameter of 16 inches. If her slice has a central angle of 45º.
