# Lesson 7 Madison’s Round Garden Develop Understanding

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

### 1.

#### a.

Volume

#### b.

Surface Area

### 2.

#### a.

Volume

#### b.

Surface Area

### 3.

#### a.

Volume

#### b.

Surface Area

### 4.

#### a.

Volume

#### b.

Surface Area

### 5.

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

### 6.

The circles have a radius of

Radius | 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.

Radius | Arc Length | Area of Sector | |
---|---|---|---|

### 9.

What is the radian measure of an angle that measures

### 10.

Refer to

#### 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.

Use the diagram for problems 11–13.

### 11.

Explain why

### 12.

If

### 13.

Find the indicated ratios.

#### a.

#### b.

#### c.

#### d.

#### e.

### 14.

The corresponding linear parts of two circles have the ratio of

Fill in the blanks.

The corresponding areas of two circles have the ratio of