Question

Question
1
Question
2
Question
3
A)
What is the area of the sector of a circle with
and a diameter of 18 inches? Write youranswer to two decimal places.
(1 point)
θ = 122°
A = π in.2
The radius is
inches.
A)
If a circle has a diameter of 20 inches, what is its radius?
(1 point)
Statement #
describes Danae’s mistake.
A)
Danae was asked to find the area of a sector with
and a radius of 23 meters. She calculated
for the area of the sector. What was her mistake?
Statement #1: She used the diameter instead of the radius.
Statement #2: She incorrectly calculated
.
Statement #3: She forgot to square the radius.
(1 point)
θ = 200°
40.14 m2
200°
360°
Question
4
Question
5
A)
A circle has a radius of 6 ft. Find the area of a sector if
. Leave your answer in terms of
.
(1 point)
θ = 150° π
A = π ft.2
Option #
describes Kelsey’s mistake.
A)
Kelsey is given a circle with a radius of 5 cm. She calculates the area of a sector that has an angle of
and provides the solution of
. What was her mistake?
Option #1: She incorrectly calculated
.
Option #2: She forgot to square the radius.
Option #3: She calculated the circumference instead of the area.
(1 point)
216° 3π cm2
216°
360°

Answer 1

Answer key:

1) Diameter = 18 in → radius = 9 in.
Area = (122/360)·π·9^2 = (122/360)·π·81 = 27.45π ≈ 86.24 in^2 (to two decimal places).

2) Diameter = 20 in → radius = 10 in.

3) Danae: Statement #3. She forgot to square the radius (her work corresponds to using 23 instead of 23^2, giving (200/360)·π·23 ≈ 40.14).

4) Radius = 6 ft, θ = 150°:
Area = (150/360)·π·6^2 = (5/12)·π·36 = 15π ft^2.

5) Kelsey: Option #2. She forgot to square the radius (gave 3π cm^2 instead of the correct 15π cm^2).