Pythagorean Theorem and Volume Review

Unit 2 Test Review (part 1)

Pythagorean Theorem

Multiple Choice

What is the area of each square?

• 2, 3, 5

• 3, 9, 18

• 9, 16, 25

• 16, 54, 91

Multiple Choice

What is the length of the hypotenuse?

• 14 cm

• 15 cm

• 13 cm

• 20 cm

Multiple Choice

What could be the areas of the other two squares?

• 576 cm2 and 625 cm2

• 245 cm2 and 290 cm2

• 301 cm2 and 620 cm2

• 224 cm2 and 518 cm2

Multiple Choice

Which of the following side lengths could form a right triangle?

• 15, 30, 45

• 7, 8, $$\sqrt[]{58}$$

• 8, 9, 10

• 5, 7, $$\sqrt[]{74}$$

​What's the measure of side a?

Multiple Choice

What is the value of a?

• 21

• 19

• 16

• 25

Multiple Choice

How high is the ramp?

• 10.1 ft

• 8.9 ft

• 9.8 ft

• 12.2 ft

Multiple Choice

How high was the tree before it fell?

• 70 ft

• 88 ft

• 50 ft

• 63 ft

Multiple Choice

A 61 ft ladder leans against a wall. It is 60 feet away from the wall at its base. How high up the wall does the ladder go?

• 48 ft

• 11 ft

• 26 ft

• 91 ft

Multiple Choice

You want to ship a piece of pipe that is 17 cm long in the box shown. Will it fit diagonally?

(Hint: Solve for the bottom triangle, then the top one.)

• Yes, you can fit it because the diagonal is about 19.2 cm long.

• No, you can't fit it because the diagonal is about 19.2 cm long.

• Yes, you can fit it because the diagonal is about 16.8 cm long.

• No, you can't fit it because the diagonal is about 16.8 cm long.

Multiple Choice

Sarah bikes 1.5 miles south, then 2 miles west to go to James' house. On the way home she rode the most direct path. ABOUT how far was her trip home?

• 5 miles

• 9 miles

• 3 miles

• 8 miles

Multiple Choice

What is the length of the hypotenuse?

• $$\sqrt[]{19}$$

• $$\sqrt[]{72}$$

• $$\sqrt[]{6}$$

• $$\sqrt[]{34}$$

Multiple Choice

What is the value of r?

• 35.2 cm

• 29 cm

• 20 cm

• 20.6 cm

Volume

Finding Volume with your scientific calculator.

1. Type the correct formula

2. Tell the calculator what r and h equal.

Multiple Choice

Find the volume of the figure. Round to the nearest tenth.

• 128.6 units³
• 1,286.1 units³
• 401.9 units³
• 5,144.6 units³

Multiple Choice

Find the volume of the cone. Round your answers to the nearest tenth. Use 3.14 for π.

• 14.13 in³

• 56.52 in³

• 169.56 in³

Multiple Choice

Find the volume of the given sphere.

• 1,563.5 cubic in.

• 1,325.5 cubic in.

• 1,129.9 cubic in.

• 1,819.6 cubic in.

Volume in terms of pi

Multiple Choice

What is the volume of the cylinder expressed in terms of pi?

$$V=\pi r^2h$$  

• $$180\pi\ cm^3$$

• $$1200\pi\ cm^3$$

• $$120\pi\ cm^3$$

• $$60\pi\ cm^3$$

Multiple Choice

What is the volume of the sphere, expressed in terms of pi?

$$V=\frac{4}{3}\pi r^3$$  

• $$81\pi\ in^3$$

• $$729\pi\ in^3$$

• $$972\pi\ in^3$$

• $$36\pi\ in^3$$

Finding the height or radius

1. Type in the formula with every given number on the graphing calculator.

2. Replace whatever letter you're solving for with an x.

Multiple Choice

The Volume of a Cone is 209.44 cm3. The radius is 5. What is the height?

• 6 cm

• 7 cm

• 8 cm

• 9 cm