Question

Tom made a circular cheesecake with a radius of 4 inches. The area of the cheesecake can be found by using the formula
A
=
π
⋅
r
2
or
A
=
π
⋅
4
2
. He cut out a piece that has a central angle of 39°, as shown below.

Triangle A-B-C with right angle at A, 60 degrees at B, and 30 degrees at C.

What is the formula for the area of the piece that Tom cut out?
A.
A
=
39
180
⋅
π
⋅
4
2

B.
A
=
39
360
⋅
π
⋅
4
2

C.
A
=
39
π
⋅
π
⋅
4
2

D.
A
=
39
2
π
⋅
π
⋅
4
2

Answer 1

Sector area = (central angle/360) × full circle area. So A = (39/360)·π·4^2, which is choice B.

(You can simplify: A = (39/360)·16π = (13/120)·16π = (26/15)π in^2 ≈ 5.44 in^2.)