Victory for the ACT Exam 16e TG Sample

U NIT 4 | G EOMETRY • 513

CIRCLES

STUDENT TEXT, p. 187 15. If the area of a circle is equal to 9 0 r , which of the following is (are) true? I I I I I I . . . T T T h h h e e e r d c a i i r a d c m i u u m e s t i f e s e r r 3 i e s . n6c.e is 6 0 r . AB .. II Ioonnl yl y C. III only D. I, II, and III

EXPLANATIONS

15. (D) Mathematics/Geometry/Circles CC: 7.G.B.4 CCRS: AVG+.G.7 Difficulty Level = 2; Teaching Time = 5–8 minutes; Purpose = Example If the area of the circle is 9 9 r r & & = = r 2 9 3 = . Thus, (I) is true. Then, if r 30 = , the diameter is 2(3) 6 = , so (II) is also true. Finally, if r 30 = , then the circumference is 2 (3) 6 = r r and (III) is true.

Don’t Forget This! 1. The 0 = . 2. The circumference of at octi hr cel ed ii as me qeut earl multiplied by r : circumference = 2 d r = r r 0 . 3. The area of a cts hqi reuc arl ear edi sdi uesq u a l t o multiplied by r : area r = r circle 2 . radius of a coinrec l-eh ai sl feoqfutahlet o diameter : r d 2

09 r , then 05 r 2 = r