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Here are a few recommended readings before getting started with this lesson.
For his birthday, Tadeo's parents are taking him to a Detroit Pistons game, his favorite NBA team. Tadeo plans to bring some money to buy souvenirs at the stadium. He asks his mother to change the coins in his piggy bank to bills to make it easier to take his money with him.
His mother tells him that the coins all have something in common. She works with Tadeo to measure the distance around the coins and the width of their faces. Tadeo then calculates the ratio of the distance around each coin to its width.A circle is the set of all the points in a plane that are equidistant from a given point. There are a few particularly notable features of a circle.
circle O,since it is centered at O.
Click on the indicated part of the given circle.
When Tadeo opened his piggy bank and compared the measures of the coins, he found that dividing the circumference by the diameter always resulted in the same number. This fact is true for all circles and is so important that mathematicians gave a unique name to this number.
π,is a constant defined as the ratio between the circumference and the diameter of a circle. This ratio is the same for all circles.
π=3.1415926…
Graphically, π is the number of times that the diameter of the circle fits on top of the circle.
Back in his room, Tadeo wants to measure the circumference of one of his coins. He does not have a tape measure and wonders whether there is another way to find the circumference of a circle. Maybe he could use a ruler? Good news! He can find this information if he knows either the circle's diameter or its radius. Remember, the diameter of a circle is twice the radius.
The circumference of a circle is calculated by multiplying its diameter by π.
C=πd
Since the diameter is twice the radius, the circumference of a circle can also be calculated by multiplying 2r by π.
C=2πr
Tadeo is finally at the Detroit Pistons stadium with his parents. During the halftime show, he was able to go onto the court for a contest. There, he realized how big the logo in the central circle is.
π≈3.14
d=12
Multiply
Round to 1 decimal place(s)
π≈3.14
r=5
Multiply
Multiply
It is the last seconds of the fourth quarter. The Detroit Pistons are about to lose by two points. Alec Burks manages to score a 2-point shot and is fouled. The clock stops at 0.2 seconds. He prepares to take a free throw. If he makes it, the Pistons will win.
π≈3.14
C=37
LHS/3.14=RHS/3.14
Rearrange equation
Calculate quotient
Round to 1 decimal place(s)
π≈3.14
C=56.5
Multiply
LHS/6.28=RHS/6.28
Rearrange equation
Calculate quotient
Round to 1 decimal place(s)
The amount of space inside a two-dimensional figure is known as the area of the figure. The area can usually be calculated if some dimensions of the figure are known. In the particular case of a circle, only its radius is needed.
When they got home from the game, Tadeo's parents gave him another birthday present. They had bought him a circular rug with the Detroit Pistons logo on it for his bedroom. Tadeo was so happy that he ran to his room and placed it on the floor next to his bed.
r=2
Calculate power
Use a calculator
Round to 2 decimal place(s)
r=10
Calculate power
Use a calculator
Round to 2 decimal place(s)
Tadeo has a cool basketball hoop-shaped clock on his bedroom wall.
The area of this clock is 144π square inches.
A=144π
LHS/π=RHS/π
Cross out common factors
Simplify quotient
Rearrange equation
LHS=RHS
a2=a
Calculate root
A semicircle is half of a circle. It is a two-dimensional figure obtained when a circle is cut into two halves. Its shape consists of an arc and a segment.
The radius of a semicircle is defined as the distance from the midpoint of the segment to any point of the arc.
The perimeter of a semicircle with radius r is the length of the segment plus half the circumference of a circle with radius r. The area of a semicircle with radius r is half the area of a circle with radius r.
Perimeter | Area |
---|---|
P=2r+πr | A=21πr2 |
Tadeo's parents bought pizza to celebrate both Tadeo's birthday and the Pistons' victory. It took Tadeo a while to get to the table because he was playing a video game. When he arrived, his parents had already eaten half of the supreme pizza.
The radius of the pizza is 6 inches.
r=6
Multiply
Commutative Property of Multiplication
r=6
Calculate power
ca⋅b=ca⋅b
ba=b/2a/2
Commutative Property of Multiplication