Mathematics, 15.04.2020 21:03 bri2576

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.

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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 ,

= $\frac{45}{360}$

$= \frac{1}{8}$ $\frac{1}{8}$

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 = $\frac{D}{2} = \frac{16}{2}$

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

= $(\frac{1}{8} )$ × 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

= $(\frac{1}{8} )$ × 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.

Answer from: Quest

108

Answer from: Quest

i don't see any steps below, sweetheart

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