Suppose you had a slice of pizza that was cut from a 16” pizza. You measure the angle that it was cut at to be 0.6 radians. EXPLAIN how you could find the length of the crust on the slice of pizza. *
C = pi*2r = 3.14 * 16in = 50.3 In.
L = (0.6rad/6.28rad) * 50.3in = 4.81 In.
NOTE: The central angle measures 0.6 radians or approximately 0.1 of a circle. Therefore, the length of the arc
is approximately 0.1 of the circumference.
To find the length of the crust on the slice of pizza, you can utilize the concept of circumference and angles. Here's an explanation of how to calculate it:
1. Understand the relationship between angles and arc length: On a circle, the circumference is divided into 2π radians (or 360 degrees). This means that if you have a full circle, the angle subtended by the entire circumference is 2π radians.
2. Calculate the circumference of the whole pizza: Since the pizza has a diameter of 16 inches, the radius would be half of that, which is 8 inches. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. Therefore, the circumference of the entire pizza is C = 2π(8) = 16π inches.
3. Understand the relationship between angle and arc length: If the angle subtended by the crust on the slice is 0.6 radians, you can find the ratio of this angle to the total angle of a full circle (2π radians).
4. Calculate the arc length: Since the total circumference of the pizza is 16π inches, the arc length of the crust on the slice can be calculated using the ratio of the angle subtended by the crust to the total angle of a full circle. This can be represented by the formula L = (θ/2π) * C, where L is the arc length, θ is the angle in radians, and C is the circumference. In this case, L = (0.6/2π) * (16π) = 0.6 * 16 = 9.6 inches.
Therefore, the length of the crust on the slice of pizza is 9.6 inches.