# Lesson 1

Solids of Rotation

• Let’s rotate two-dimensional shapes to make three-dimensional shapes.

### Problem 1

Sketch the solid of rotation formed by rotating the given two-dimensional figure using the horizontal line shown as an axis of rotation.

### Problem 2

Draw a two-dimensional figure that could be rotated using a vertical axis of rotation to give the barrel shown.

### Problem 3

Match the two-dimensional figure and axis of rotation with the solid of rotation that can be formed by rotating the figure using that axis.

### Problem 4

Find the area of the shaded region.

(From Unit 4, Lesson 11.)

### Problem 5

Technology required. Find the area of the figure.

(From Unit 4, Lesson 11.)

### Problem 6

Technology required. This stop sign is a regular octagon. It has side lengths of 12 inches. What is the area? What is the perimeter?

(From Unit 4, Lesson 10.)

### Problem 7

Right triangle $$ABC$$ is shown.

Select all expressions which are equal to the length of side $$BC$$.

A:

$$\sqrt{4.9^2+6^2}$$

B:

$$\sqrt{6^2-4.9^2}$$

C:

$$4.9\sin(55)$$

D:

$$\frac{4.9}{\sin(55)}$$

E:

$$4.9\tan(55)$$

F:

$$\frac{4.9}{\tan(55)}$$

G:

$$6\cos(55)$$

H:

$$\frac{6}{\cos(55)}$$

(From Unit 4, Lesson 6.)