Lesson 2 Any Way You Spin It Develop Understanding

Ready

Use the given measures on the triangles to write the indicated trigonometric value. Then find the measure of the indicated angle to the nearest $100 th$ of a degree.

1.

$\sin P =$

$\cos P =$

$\tan P =$

$m ∠ P =$

2.

$\sin N =$

$\cos N =$

$\tan N =$

$m ∠ N =$

3.

$\sin B =$

$\cos B =$

$\tan B =$

$m ∠ B =$

4.

$\sin A =$

$\cos A =$

$\tan A =$

$m ∠ A =$

Set

Rotate each 2-D shape about the $x$ -axis. Draw a sketch of the 3-D object that would be formed or name the object.

5.

6.

7.

8.

9.

Name something in the world that would be shaped like the solid of revolution formed if the figure shown were rotated about the $y$ -axis.

10.

a.

Name something in your house that would be shaped like the solid of revolution formed, if the figure shown were rotated about the $x$ -axis.

b.

Calculate the volume of the shape that has been rotated about the $x$ -axis.

$V = π r^{2} h$

Go

Find the volume of the indicated solid.

11.

$V = π r^{2} h cylinder$

$r = 3 inches$

$h = 10 inches$

12.

$V = \frac{1}{3} B H$ right circular cone

$r = 8 cm$

$H = 20 cm$

13.

$V = \frac{1}{3} s^{2} h$ square pyramid

$h = \frac{5 \sqrt{2}}{2} m$

$s = 3 \sqrt{5} m$

The base is a square.

14.

$V = \frac{1}{3} h (a^{2} + a b + b^{2})$ square frustum, where $a$ and $b$ are the base and top side lengths and $h$ is the height.

$h = 12 in.$

$a = 5 \sqrt{7} in.$

$b = 2 \sqrt{7} in.$