Honors Geometry
Areas of circles & other shapes
Circumference: C = 2πR where R is the radius.
C = πD where D is the diameter.
2
Area: A=π R
R
Sectors: The area of a sector is just the fractional
part of the entire area of the circle that its central
angle represents.
Sector area: A 
Name ______________________
Worksheet 7.1
R
xº
x
R2
360
Show all relevant work on the following problems:
1. Find the area of a circle of radius 8.
2. Find the radius of a circle if the area is:
a. 1000
b. 4096π
3. Find the area of a circle if the circumference is:
a. 64
c. 12π
4. Find the area of each shaded sector
a.
b.
74º
2
c. Find the perimeter of each sector
15
5. These are squares with sides of length 24 and
congruent circles just fit in each of them. For each
figure find the percent of the square which is
empty space not occupied by a circle.
24
24
Explain your result.
6. Circular sectors are placed at the corners of this
square of side10. What is the area left over in the
center?
10
7. Find the area of the shaded region which
consists of a circle of diameter 20 with two
congruent circles just fitting along the diameter.
8. a) The shaded area shown is called a segment.
It is what is left of the sector of a circle when the
triangular portion is removed. Find its area.
9
b) Find the perimeter of the segment
9. Find the area of the segment bounded by
segment BC(which has length 12) and circle A.
B
12
A
C
12
24
10. A cone is formed from a sector of a circle of radius 10. The arc length of the sector is 15  . Find
the volume and surface area of the cone.
11. Find the radius of a cone which is formed by a sector of central angle  radians, from a circle of
radius R.
12. Find the radius of the inscribed circle of a right triangle with legs of length, 8 & 15.