# 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.

### Problem 5

*Technology required. *Find the area of the figure.

### 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?

### Problem 7

Right triangle \(ABC\) is shown.

Select **all** expressions which are equal to the length of side \(BC\).

\(\sqrt{4.9^2+6^2}\)

\(\sqrt{6^2-4.9^2}\)

\(4.9\sin(55)\)

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

\(4.9\tan(55)\)

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

\(6\cos(55)\)

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