Pythagorean Theorem & Volume

Pythagorean Theorem & Volume

Unit 4​

By Kristin Harrell

The Pythagorean Theorem

Hypotenuse

• The longest side of a right triangle

• The side that is opposite (across) from the 90^o angle.

• When using the Pythagorean Theorem, the Hypotenuse is represented by the variable, c.

Is it a Right Triangle?

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is a triangle with side lengths of 12, 9, and 15 a right triangle?

• Yes

• No

Multiple Choice

Is a triangle with side lengths of 7, 4, and 4 a right triangle?

• Yes

• No

Multiple Choice

Find the missing side.

• 18

• 16

• 17

• 19

Multiple Choice

Find the missing side.

• 11

• 12

• 13

• 14

Multiple Choice

A triangle has legs that are 7 inches and 24 inches long. How long is the hypotenuse?

• 23

• 26

• 28

• 25

Multiple Choice

In a right triangle, if a = 8 and c = 17, what is the correct setup to find the value of b?

• $$17^2+8^2=b^2$$

• $$8^2+b^2=17^2$$

• $$17^2+b^2=8^2$$

• $$\frac{8^2}{b^2}=\frac{17^2}{100}$$

Multiple Choice

Level 3

Find the length of the missing side.

• 20 in.

• 68 in.

• 16 in.

• 80 in.

Multiple Choice

Shay’s garden is in the shape of a right triangle. The hypotenuse is 15 feet, and the longer leg is 3 feet more

than the shorter leg. What are the lengths of the two legs?

• The lengths of the legs of Shay’s triangular garden are 7 feet and 10 feet.

• The lengths of the legs of Shay’s triangular garden are 8 feet and 11 feet.

• The lengths of the legs of Shay’s triangular garden are 9 feet and 12 feet.

Volume of Cylinder

Multiple Choice

Find the volume of the cylinder.

• 4239

• 1696

• 1130

• 565

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

What's the volume of the cylinder?

• $$V=588\pi$$

• $$V=1008\pi$$

• $$V=168\pi$$

• $$V=1846\pi$$

Multiple Choice

A can of pasta has a diameter of 3 inches and a Volume of 50 cubic inches of sauce. What is the height of the can? Round your answer to the nearest tenth.

• 1.8 inches

• 5.3 inches

• 10.6 inches

• 7.1inches

Multiple Choice

 A cylinder has a height of 12 inches and a radius of 2.5 inches. What is the volume of the cylinder? Use 3.14 for pi and Round your answer to the nearest tenth. 

• $$V=188.4\ in^3$$  

• $$V=235.5\ in^3$$  

• $$V=75\ in^3$$  

• $$V=94.2\ in^3$$  

Volume of Cone

Multiple Choice

V = ?

• 14.13 in³
• 56.52 in³
• 169.56 in³

Multiple Choice

v = ?

• 2,144.66 m³
• 1,608.49 m³
• 536.17 m³
• 498.62 m³

Multiple Choice

find the volume. Round to the nearest hundredth.

• 1526.82mi

• 1326cm³

• 6104.16mi³

• 1026.04mi³

Multiple Choice

What is the volume of the cone?

• 107 in³

• 480 in³

• 160 in³

• 53 in³

Multiple Choice

• $$18.67\pi\ cm^3$$

• $$32.67\pi\ cm^3$$

• $$98\pi\ cm^3$$

• $$175.84\pi\ cm^3$$

Multiple Choice

$$A\ cone\ has\ a\ volume\ of\ 320\pi\ mm^3\ and\ a\ base\ radius\ of\ 9mm.$$  What is the height of the cone? Round the the nearest whole number.

• 10 mm

• 9 mm

• 12 mm

• 11 mm

Volume of Spheres

Multiple Choice

Find the Volume of the Sphere

• 904.32 ft³
• 7,234.56 ft³
• 150.72 ft³

Multiple Choice

Find the volume of the sphere. Use 3.14 for $$\pi$$ .  Round to nearest tenth.

• 78.5 $$m^3$$  

• 392.5 $$m^3$$  

• 523.3  $$m^3$$  

• 62.8  $$m^3$$  

Multiple Choice

A golf ball has a diameter of 1.68 inches. What is the volume of the golf ball? Use 3.14 for pi and round your answer to the nearest hundredth.

• 19.85 in³

• 2.95 in³

• 2.48 in³

• 11.82 in³

Multiple Choice

An inflated spherical shaped balloom is filled with 112 in³ of air. What is the radius of the balloon? Use 3.14 for pi and round your answer to the nearest inch.

• 3 in

• 5 in

• 2 in

• 4 in

Multiple Choice

What is the volume of the sphere? Round your answer to the nearest tenth.

• 1071.8 ft³

• 200.9 ft³

• 4287.1 ft³

• 17,148.6 ft³

Multiple Choice

Find the volume of the hemisphere. Use 3.14 for pi and round your answer to the nearest tenths.

• 523.3 yd³

• 32.7 yd³

• 65.4 yd³

• 87.2 yd³