Chapter 3 - Circles & Cylinders

Question 1

How many degrees are in a circle?

Answer 1

a circle has 360 degrees.

Question 2

Any line segment that connects the center point to a point on the circle is?

Answer 2

radius

Question 3

Any line segment that connects two points on a circle is?

Answer 3

chord

Question 4

Any chord that passes through the center of the circle is called?

Answer 4

diameter.

diameter is twice the length of the radius

Question 5

What is circumference and its formula?

Answer 5

C= Circumference is the distance AROUND a circle.

Circumference is also a full revolution or turn of a spinning wheel going around once.

C= πd or C= 2πr

Question 6

What is diameter and its formula?

Answer 6

The distance across a circle

Diameter=2r

Question 7

What is radius?

Answer 7

Half the distance across a circle

Question 8

What is the area of the circle?

Answer 8

The space inside a circle is the area of the circle.

Area= πr²

Question 9

What is the length of arc AXB with a central angle of 60 degrees and radius of 12?

Answer 9

There are 2 steps to find out the arc length? **

Circumference and Arc length are correlated so when you are asked to find out arc length, think of C and Arc length together.

Step 1) = Find out the circumference of the circle using formula C=2πr or πd. If r is 12, C= 2π12 = C= 24π

Step 2) Use the central angle to determine what fraction the arc is of the entire circle. If the central angle is 60 and the entire circle is 360 than 60/360 = 1/6 of the circe.

Lastly, the measure of arc AXB is 1/6 * 24π= 4π

Question 10

How to find the perimeter of a sector?

Answer 10

Think of a sector as a slice of pizza where the arc corresponds to the crust and the tip corresponds to the tip of the pizza slice.

Step 1). Find the Arc length of the circle by first finding out the circumference of the circle and finding out the central angle of the circle. Than multiply both circumference and central angle to find out the arc length

Step 2). Once you have the arc length, add the arc length and 2 sides (which are the radius) to find out the perimeter of the sector.

Question 11

What is the area of sector ACB with a central angle of 60 degrees and radius of 3?

Answer 11

1) First find the area of the entire circle

Area of a circle = π(r)²

Area of a circle = π(3)²

Area of a circle = π(9)

2) Use the central angle to determine the fraction of the entire circle represented by the sector. 60/360=1/6

Therefore, area of sector is 1/6*9π = 1.5π

Question 12

What is a central angle?

Answer 12

A central angle is an angle whose vertex lies at the center point of a circle

Question 13

What is an inscribed angle?

Answer 13

An inscribed angle has its vertex on the circle itself unlike the central angle which has its vertex in the center of the circle.

**Inscribed angle is also equal to half of the arc it represents. So if the arc is 60 degrees, the inscribed is 30 degrees.

Question 14

What are inscribed triangles?

Answer 14

A triangle is said to be inscribed in a circle if all of its vertices of the triangle are points on the circle.

IMP Rule: If one of the sides of an inscribed triangle is a DIAMETER of the circle, then the triangle MUST be a right triangle.

Conversely, any right triangle in a circle must have the diameter of the circle as one of its sides (thereby splitting the circle in half)

Question 15

What is the surface area of a cylinder?

Answer 15

SA= 2 circles + rectangle= 2(πr²) + 2πrh

Question 16

What is the formula for volume of a cylinder?

Answer 16

Volume of a cylinder measures how much “stuff” it an hold inside.

V=πr²h