Question

Please Show All Work!!

1.)You are going to eat a slice of pizza, where the central angle of your slice is 34° and the radius of your slice is 8".
What is the angle in radians? Use 3.14 for pi

A.) .72 radians
B.) 2.3 radians
C.) .59 radians
D.) .48 radians

2.) Calculate the area of the sector (the slice you eat). Round your answer to the nearest tenth. Use 3.14 for pi.

Area = n/360 * π r^2
n is your central angle in degrees.

3.) Calculate the arc length of the pizza you have eaten. Use 3.14 for pi. Ø is the angle in degrees

Arc Length = 2πr * Ø/360

Answer 1

To find the angle in radians, we need to convert the given angle from degrees to radians. We know that 180 degrees = π radians.

So,

34 degrees = (34/180) * π radians

= 0.1885 * 3.14

= 0.591 radians

Therefore, the answer is (C) 0.59 radians.

The area of the sector (the slice you eat) can be calculated using the formula:

Area = (n/360) * πr^2

where n is the central angle in degrees, and r is the radius of the slice.

Plugging in the given values, we get:

Area = (34/360) * 3.14 * 8^2

= 0.1 * 3.14 * 64

= 20.096 square inches

Rounding to the nearest tenth, the answer is 20.1 square inches.

The arc length of the pizza you have eaten can be calculated using the formula:

Arc Length = (2πr * Ø)/360

where Ø is the angle in degrees, and r is the radius of the slice.

Plugging in the given values, we get:

Arc Length = (2 * 3.14 * 8 * 34)/360

= 4.776 inches

Therefore, the answer is 4.776 inches.