a) The length of the outside of one piece of birthday cake is 3.64
b) The area of one piece is 12.8
Explanation:
The given information are,
- A birthday cake has a circumference of 14π.
- The slices are cut at 30 degree angles.
- The birthday cake is in the shape of a circle.
The formula for the circumference of the circle is 2πr.
⇒ 2πr = 14π
⇒ 2r = 14
⇒ r = 14/2
⇒ r = 7
The radius of the birthday cake is 7.
To find the length of outside of one piece :
Length of the arc = (central angle / 360) × 2πr
⇒ (30/360) × 14π
⇒ (1/12) × 14π
⇒ (7/6)π
⇒ 1.16 × 3.14
⇒ 3.64
Therefore, the length of the outside of one piece of birthday cake is 3.64
To find the area of one piece :
Area of the arc = (central angle / 360) × πr²
⇒ (30/360) × π(7)²
⇒ (1/12) × 49π
⇒ (49/12) × (3.14)
⇒ 4.08 × 3.14
⇒ 12.8
Therefore, the area of one piece is 12.8