Question

5) Suppose a slice of a 12-inch pizza has an area of 20 square inches. What is the angle of
this slice?
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Answer 1

Answer:

The angle of slice is approximately 16°.

Step-by-step explanation:

The slice of pizza represent the sector of a circle.

The area of a sector is:

$A=\frac{1}{2}r^{2}\phi$

Here,

r = radius of the circle

Φ = angle in radians

Given:

A = 20 inches²

r = 12 inch

Compute the angle of the slice as follows:

$A=\frac{1}{2}r^{2}\phi$

$\phi=\frac{2\times A}{r^{2}}$

  $=\frac{2\times 20}{12\times 12}\\\\=0.2778$

The angle us 0.2778 radians.

Convert the angle into degrees as follows:

$\text{Angle}=0.2778\times\frac{180}{\pi}=15.9168\approx 16^{o}$

Thus, the angle of slice is approximately 16°.