A birthday cake has a circumference of 14n.

The slices are cut at 30 degree angles.

a) What is the length of the outside of one

piece of birthday cake?

b) What is the area of one piece?

a) The length of the outside of one piece of birthday cake is 3.64

b) The area of one piece is 12.8

Step-by-step 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