# Lesson 4Madison’s Round GardenDevelop Understanding

Find the volume and surface area for each 3-D shape.

Volume

Surface Area

Volume

Surface Area

Volume

Surface Area

Volume

Surface Area

## Set

### 5.

Circle has a radius of and a circumference of or about . Segment is the diameter of the circle.

#### a.

What is the degree measure of arc ?

#### b.

What is the length of arc ?

#### c.

What is the ratio of the length of to the length of the radius?

### 6.

The circles have a radius of , , , and units, respectively. The diameter divides each circle into two equal sectors. Find the arc length of one half of each of these circles. Then fill in the table with the indicated values.

Arc Length

Radian Measure of Central Angle

### 7.

Why does the arc length increase as the radius increases, but the ratio of arc length to the radius remains the same?

### 8.

Each circle has a different radius. Fill in the chart with the indicated values.

Arc Length

Area of Sector

### 9.

What is the radian measure of an angle that measures ?

### 10.

Refer to in (problem 8).

#### a.

How many multiples of this arc would be needed to be equal to the length of the entire circumference of circle ?

#### b.

Would this be true for the other arcs and circles in problem 8? Explain your thinking.

## Go

Use the diagram for problems 11–13.

### 11.

Explain why is similar to . (Include center of dilation and scale in your explanation.)

### 12.

If is the pre-image and is the image, how would the scale factor be different?

### 13.

Find the indicated ratios.

### 14.

The corresponding linear parts of two circles have the ratio of to the scale factor or .

Fill in the blanks.

The corresponding areas of two circles have the ratio of to the or .