Page 241 - Algebra 1

g. Find the ratio of the volumes. How does this ratio compare to the scale factor?
Application: Changing Dimensions
A dartboard is composed of concentric circles.
The radius of the smallest inner circle is 1 inch,
and with each consecutive circle, the radius
increases by 1 inch. 1
a. What is the ratio of the circumference of the two inner circles to the circumference of the outermost circle?
circumference of outermost circle 2π(5) 5
b. What is the ratio of the area of the two inner circles to the area of the
Ratios of the Perimeter, Area, and Volume of Similar Figures
If two similar figures have a scale factor of _a , then the ratio of their _a _a2 b
perimeters is b , the ratio of their areas is b2 , and the ratio of their
volumes is _a3 . b3
Example
4
Math Language
Perimeter is the distance around a closed plane figure. Circumference
is the distance around a circle.
SOLUTION
circumference of two inner circles = 2π(2) = 2 _____
outermost circle?
area of outermost circle π(5)2 = _4 π
25π = _4
25
a. ΔABC ∼ ΔLKM. Find m∠K and m∠C. (Ex 1)
SOLUTION
area of two inner circles = π(2) ____2
Math Reasoning
Verify Use Example 3
to show that if similar
figures have a scale
factor of _a , then the ratio
b _a2 of their areas is b2 .
Lesson Practice
226 Saxon Algebra 1
(Ex 1)
to find x.
B
b. The figures are similar. Find the scale factor. Then use the scale factor
5 feet
25°
K
135°
20°
ACLM
x
3 feet
5 feet