Page 34 - Algebra 1

Example
4
Application: Comparing a Crop Circle to a Soccer Field
A crop circle in a wheat field has a diameter of 100 yards. Its area is
_2 100
SOLUTION
Hint
Remember that the formula for the area of a circle is πr2.
3.14 · ( 2 ) square yards. A World Cup soccer field is 70 yards by
110 yards. Its area is (70 · 110) square yards. How much larger is the crop circle than the soccer field?
Find each area and subtract to find the difference. _100 2
Areaofcropcircle:3.14·(2 ) Area of soccer field: (70 · 110)
_1002( ) Differenceinarea:3.14·( 2 )- 70·110
Evaluate inside the parentheses. Simplify the exponent.
Multiply.
Subtract.
Simplify the expression. _100 2
3.14·(2 )-(70·110)
= 3.14 · (50)2 - (7700) = 3.14 · 2500 -7700
= 7850 - 7700
= 150
The crop circle is 150 yd2 larger than the soccer field.
a. Simplify 45 - (2 + 4) · 5 - 3. Justify each step. (Ex 1)
Simplify each expression. Justify each step.
(Ex 2)
b.
c.
d.
(Ex 3)
e.
(Ex 4)
Lesson Practice
9·23 -9÷3 15-3 +4·2
_ 2_ 7
Compare the expressions. Use <, >, or =. _1 +32 +6 5-2+2·4+3÷9
Caution
Do not forget to cube _3 2
in the expression for the model moon’s volume.
4
Jonah is making a model of the moon using plastic foam. He uses
the formula _4 πr3 to find the volume. The model moon’s radius _3 3
is 2 inches. What is the volume of the model moon? Give the answer in terms of π.
Lesson 4 19