Question

If
and
, then what is the scale factor of circle
x
to circle
y
?
(1 point)
x = 15 y = 50
3
10
9
10
3
5
3
13

A)
If the diameter of Earth is 7,918 mi., then what is its circumference to the nearest mile?
(1 point)
24,875 mi.
12,438 mi.
2,520 mi.
49,750 mi.
A)
What is the area of a circle with a diameter of 8 inches?
(1 point)
25
in.
2
50
in.
2
158
in.
2
13
in.

A)
If the length of an arc of a circle is 44 inches and the radius is 12 inches, then what is the degreemeasure of the central angle to the nearest tenth of a degree?
(1 point)
210.1 degrees
4.6 degrees
420.2 degrees
308.4 degrees

A)
If the diameter of a circle is 30 inches and a central angle of
creates a major arc, then how long isthat arc?
(1 point)
7π
4
26.25 in.
49 in.
52.5 in.
82.5 in.
A)
What is the area of the sector of a circle with
and a radius of 6 cm? Include pi in yourcalculation.
(1 point)
θ = 115°
A
=
36.13
cm
2
A
=
113.10
cm
2
A
=
76.97
cm
2
A
=
6.02
cm
2

A)
A pool has a diameter of 18 ft. Pam wants to block off a section of the pool at an angle of 75°. Whatwill be the area of the section that is blocked off? Round your answer to the nearest thousandths.
(1 point)
A
=
64.125
π
ft.
2
A
=
81
π
ft.
2
A
=
67.5
π
ft.
2
A
=
16.875
π
ft.
2

Answer 1

Here are the answers (with brief work):

1) Scale factor of circle x to circle y when x = 15 and y = 50:
- 15/50 = 3/10.

2) Circumference of Earth (d = 7,918 mi):
- C = πd = π(7,918) ≈ 24,875 mi.

3) Area of circle with diameter 8 in (r = 4 in):
- A = πr^2 = 16π ≈ 50.27 in^2 → 50 in^2 (closest given).

4) If arc length = 44 in and r = 12 in, central angle in degrees:
- θ (rad) = s/r = 44/12 = 11/3 rad. θ° = (11/3)(180/π) ≈ 210.1°.

5) Diameter = 30 in; a central angle that produces the major arc (interpreting the given as a 45° central angle producing a 315° major arc):
- Arc length = (315/360)·(30π) = 26.25π ≈ 82.5 in → 82.5 in.

6) Area of sector with θ = 115° and r = 6 cm:
- A = (115/360)·π·6^2 = 11.5π ≈ 36.13 cm^2.

7) Pool diameter 18 ft, sector with central angle 75°:
- r = 9 ft; A = (75/360)·π·9^2 = 16.875π ≈ 52.997 ft^2 (16.875π ft^2).