if the radius of a pizza is 20cm what is the central angle in degrees that gives one person 30 cm of crust
C = 2pi*r = 6.8*20 = 136 cm
136/360 = 30/A
A = 79.4 deg.
To find the central angle that gives one person 30 cm of crust on a pizza with a 20 cm radius, you can use the formula for the arc length of a circle:
Arc Length = Radius * Central Angle
In this case, we want the arc length (30 cm) and the radius is given (20 cm). Let's substitute these values into the formula:
30 cm = 20 cm * Central Angle
Now we can solve for the central angle:
Central Angle = 30 cm / 20 cm
Central Angle = 1.5
So, the central angle that gives one person 30 cm of crust on a pizza with a 20 cm radius is approximately 1.5 radians.
To find the central angle in degrees that gives one person 30 cm of crust on a pizza with a radius of 20 cm, you can follow these steps:
1. Recall that the circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.
2. Calculate the circumference of the pizza by substituting the given radius into the formula: C = 2π × 20 = 40π cm.
3. Since one person is getting 30 cm of crust, we need to find the angle that corresponds to this portion of the circumference. To do this, we will use the proportion between the length of the crust and the total circumference:
(Angle in degrees) / 360 = (Length of crust) / (Total circumference)
Let x represent the angle in degrees. So the equation becomes: x / 360 = 30 / (40π).
4. Solve for x by cross-multiplying and simplifying the equation:
x = (360 * 30) / (40π) ≈ 68.18 degrees.
Therefore, the central angle in degrees that gives one person 30 cm of crust on a pizza with a radius of 20 cm is approximately 68.18 degrees.