Circles

Words of “Wiz-dom”-The key to circle problems is the radius. All other measurements (diameter, circumference, and area) rely on it. So if you are given the radius, you can calculate everything else. If you are given anything else, you can calculate the radius. Do the following review problems.

O is the center of the circle. The radius is 3.

What is the diameter? Answer #1

What is the circumference? Answer #2

What is the area? Answer #3

Words of “Wiz-dom”-The test writer expects you to know a tangent to a circle is a line that barely touches a circle and is at a right angle to a radius that touches the same spot. For example in the above diagram AC is tangent to the circle at point B. The angle formed by AB and the radius is a right angle.

Words of “Wiz-dom”-The other issue the test writer wants to test is whether you understand that there are 360 degrees in a circle. Of course, this leads to applying rules related to portions of the area of a circle and the arcs of a circumference based on the number of degrees where two radii intersect. The formula looks like the following:

Answer the following review questions.

What is the diameter? Answer #4

What is the circumference? Answer #5

What is the area? Answer #6

What is the length of arc ABC? Answer #7

What is the area of the wedge OABC? Answer #8

Sample Questions

1. If the diameter of the circle O is 8, what is the area of the shaded region?

A.
B.
C.
D.
E. 

Answer to question #1

 

2. In the diagram above, the area of the circle is π. What is the area of the square?(A) 1(B) 2(C) 4(D) 8

(E) 12

Answer to question #2

3. A 16-inch (diameter) pizza is cut into 8 equal slices. What is the perimeter of the one slice that Ms. Wiz ate?(A)
(B)
(C)
(D)
(E) 

Answer to question #3

4. A 16-inch (diameter) pizza is cut into 8 equal slices. What is the sum of the angles at the center of the pizza for the three pieces that were eaten by The Wiz?A. 90
B. 100
C. 105
D. 120
E. 135

Answer to question #4

REVELATIONS: Demystifying the ACT is available for the exclusive use of students who have registered through MaxTheTest.com or attend a school which is licensed to distribute it. Any distribution or use of these materials beyond these students or schools by any individual or organization and/or removal of this notice is a violation of federal copyright laws.