Question

PLS HELP: Sonya chooses a slice from another pizza that has a diameter of 16 inches. If her slice has a central angle of 45º what is the area of her slice? What is the length of its crust? Show how you calculated your answers.

Answer 1

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.

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 ,

=
`(45)/(360)`

`= (1)/(8)`
`(1)/(8)`

Area of Pizza is, (pizza is a circular shape),

`A = \pi r^(2)`..............................(1)

Where, r - Radius of pizza

From given,

Diameter, D = 16 inches

r =
`(D)/(2) = (16)/(2)`

r = 8 inches

Equation (1) becomes,

`A = \pi 8^(2)`

`= (3.14)(64)` (∵
`\pi =3.1415` )

= 201.0619 square inches

Area of pizza slice,

= Ratio of slice to pizza × Area of pizza

=
`((1)/(8) )` × 201.0619

= 25.133 square inches

Area of pizza slice = 25.133 square inches

Step:2

Formula for perimeter of pizza,

`P = 2\pi r`................................(2)

Where, r - Radius of pizza

From given, r = 8 inches

Equation (2) becomes,

`= 2 (3.1415)(8)` (∵
`\pi =3.1415` )

= 50.265 inches

Perimeter of slice is,

= Ratio of slice to pizza × Perimeter of pizza

=
`((1)/(8) )` × 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.