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

The angle of slice is approximately 16°.

Explanation:

The slice of pizza represent the sector of a circle.

The area of a sector is:

`A=(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=(1)/(2)r^(2)\phi`

`\phi=(2* A)/(r^(2))`

`=(2* 20)/(12* 12)\\\\=0.2778`

The angle us 0.2778 radians.

Convert the angle into degrees as follows:

`\text{Angle}=0.2778*(180)/(\pi)=15.9168\approx 16^(o)`

Thus, the angle of slice is approximately 16°.