Lesson on Circles

Everything You Wanted to Know about Circles - Almost

Dr. Tom Giles

​Math Antics Circles, Circumference, & Area

Multiple Choice

The radius of this pizza is 9 ½ in. What is the approximate area of the pizza?

• 81 in²

• 29.83 in²

• 59 ⅔ in²

• 283 ½ in²

Multiple Choice

What is the area of a circle?

• The distance around a circle.
• The space inside the circle.
• A line from side to side passing through the center.
• A line from the center to the side.

Multiple Choice

What is the formula to find the area of a circle?

• A = πd

• A = 2πr

• A = πr²

• A = xyz

Multiple Choice

Find the area of the circle

• 43.96
• 153.86
• 87.82
• 307.72

Multiple Choice

Find the area of the circle in the picture.

• 34.54 in²

• 69.08 in²

• 379.94 in²

• 254.34 in²

Multiple Choice

What is circumference?

• The distance around a circle.
• The space inside the circle.
• A line from side to side passing through the center.
• A line from the center to the side.

Multiple Choice

Find the circumference of the circle

• 87.82
• 153.86
• 43.96
• 307.72

Multiple Choice

The circumference of a circle is 28.26 cm. What is closest to the area of the circle.

• 254.34 cm²

• 14.13 cm²

• 63.6 cm²

Multiple Choice

The circumference of a circle is 37.68 yds. What is the diameter? Use 3.14 for Pi.

• 118.3 yds

• 6 yds

• 12 yds

• 59.5 yds

Multiple Choice

The diameter of the wheel on a bicycle is 24 inches. Which is closest to the circumference of the wheel?

• 25.36 in

• 37.68 in

• 75.36 in

• 452.16 in

From the Equation

• Make the signs on h and k OPPOSITE to get the center

• Take the SQUARE ROOT of r² to get the radius

• If you don't SEE a h or k, then that means the coordinate is ZERO.

Multiple Choice

Write the equation of the circle with center (-4, 0) and a diameter of 10.

• $$\left(x-4\right)^2+y^2=100$$  

• $$\left(x+4\right)^2+y^2=100$$  
  

• $$\left(x+4\right)^2+y^2=25$$  

• $$x^2+\left(y+4\right)^2=25$$  

• $$\left(x-4\right)^2+y^2=25$$  

Multiple Choice

Write the equation of the circle with center (2, -9) and a diameter of $$\sqrt{11}$$  .

• $$\left(x+2\right)^2+\left(y-9\right)^2=11$$  

• $$\left(x-2\right)^2+\left(y+9\right)^2=11$$  

• $$\left(x+9\right)^2+\left(y-2\right)^2=11$$  

• $$\left(x-9\right)^2+\left(y+2\right)^2=11$$  

Multiple Choice

$$\left(x+3\right)^2+\left(y+7\right)^2=4$$

What is the radius and center of the circle

• r = 4,  (3, 7)
  

• r = 4, (-3, -7)
  

• r = 2, (3, 7)
  

• r = 2, (-3, -7)
  

Multiple Choice

Find the equation of the circle.

• $$x^2+y^2=12$$

• $$x^2+y^2=144$$

• $$x^2+y^2=36$$

• $$x^2+y^2=576$$

Multiple Choice

Which of the following is the equation of a circle with a center at (-1,3) and a radius of 4?

• (x-1)²+(y+3)²=4

• (x-1)²+(y+3)²=16

• (x+1)²+(y-3)²=4

• (x+1)²+(y-3)²=16

Multiple Choice

Which is the correct equation for the circle?

• (x-3)²-(y+1)²=8

• (x-3)²+(y+1)²=8

• (x+3)²+(y-1)²=16

• (x-3)²-(y+1)²=16

• (x-3)²+(y+1)²=16

Multiple Choice

Which is the correct equation for the circle?

• (x+5)²+(y+2)²=9

• (x-2)²+(y-5)²=9

• (x+2)²+(y+5)²=9

• (x+2)²+(y+5)²=3

• (x-2)²+(y-5)²=6

Multiple Choice

What is the equation of this circle?

• (x - 2)² + (y - 1)² = 4

• (x + 2)²+(y + 1)²=16

• (x + 2)² + (y - 1)² = 4

• (x + 2)²+(y - 1)²=16

Multiple Choice

Write the equation of the circle with center C( -5, 8 ) and radius = 7.

• ( x - 5 )² + ( y + 8 )² = 14

• ( x - 5 )² + ( y - 8 )² = 49

• ( x - 5 )² + ( y + 8 )² = 49

• ( x + 5 )² + ( y - 8 )² = 49

Multiple Choice

Identify the center and radius of a circle with the following equation: $$\left(x+7\right)^2+\left(y-5\right)^2=16$$  

• Center (7, -5) & Radius = 16

• Center (-7, 5) & Radius = 8

• Center (7, -5) & Radius = 4

• Center (-7, 5) & Radius = 4

Multiple Choice

Identify the center and radius of a circle with the following equation: $$\left(x+5\right)^2+\left(y+2\right)^2=48$$  

• Center (5, 2) & Radius = 24

• Center (-5, -2) & Radius  $$\approx$$  6.93

• Center (5, 2) & Radius = 48

• Center (-5, -2) & Radius = 24

Multiple Choice

Which is the correct standard equation of a circle with the given information? Center: (-3, 2) and Radius = 16

• $$\left(x-3\right)^2+\left(y+2\right)^2=256$$

• $$\left(x+3\right)^2+\left(y-2\right)^2=4$$

• $$\left(x+3\right)^2+\left(y-2\right)^2=256$$

• $$\left(x-3\right)^2+\left(y+2\right)^2=16$$

Multiple Choice

Which is the correct standard equation of a circle with the given information? Center (7, -2) and passes through (-1, -6)

• $$\left(x-7\right)^2+\left(y+2\right)^2=6,400$$

• $$\left(x+7\right)^2+\left(y-2\right)^2=80$$

• $$\left(x+1\right)^2+\left(y+6\right)^2=6,400$$

• $$\left(x-7\right)^2+\left(y+2\right)^2=80$$

Multiple Choice

A circle has a center at (1, 1). The diameter is 6. Which of the following points is a point on the circle?

• $$\left(0,\ -1\right)$$

• $$\left(-1,\ 3\right)$$

• $$\left(4,\ 1\right)$$

• $$\left(3,\ 3\right)$$

Multiple Choice

A circle has the equation x² + y² - 12x + 8y + 3 = 0. Write the equation in standard form.

• (x - 6)² + (y + 4)² = 49

• (x + 4)² + (y - 6)² = 49

• (x - 6)² + (y + 4)² = 55

• x² + y² = 55

Multiple Choice

The equation of a circle is x² + y² + 6x - 12y + 20 = 0. Write the equation in standard form.

• (x - 3)² + (y + 6)² = 25

• (x + 3)² + (y - 6)² = 25

• (x - 3)² + (y + 6)² = 45

• (x + 3)² + (y - 6)² = 5

Multiple Choice

A circle has the equation x² + y² + 10x - 4y + 20 = 0. Write it in standard form.

• (x - 5)² + (y + 2)² = 9

• (x + 5)² + (y - 2)² = 3

• (x + 5)² + (y - 2)² = 9

• (x - 5)² + (y + 2)² = 3

Multiple Choice

Find the center and radius of the circle: x² + y² + 14x - 2y = -1.

• center = (-7, 2) radius = 3

• center = (-7, 1) radius = 7

• center = (-4, 1) radius = 7

• center = (-4, 2) radius = 3

Multiple Choice

Determine the center and radius:
x² + y² - 10x + 8y -8 = 0

• C = (5,-4) r = 7
• C = (-5,4) r = 7
• C = (-4,5) r = 49
• C = (5,-4) r = 49