Unit 5 Circles and Volume

Unit 5 Circles and Volume

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Area of a circle is the amount of space inside the circle.

To calculate area of a circle we multiply 3.14 x radius²

That means we multiply the radius x itself first!

Multiple Choice

find the area of the circle below.

• 100 cm
• 225 cm
• 9 cm
• 28.26 cm

Multiple Choice

find the area of the circle below.

• 100 cm
• 225 cm
• 9 cm
• 28.26 cm

Multiple Choice

Shring's dining room table is round and has a radius of 4.5 feet. What is the tabletop's area?

• 63.585 ft²
• 68.345 ft²
• 64.585 ft²
• 61.345 ft²

Multiple Choice

A cruise ship has a large, circular window. It has a diameter of 6 meters. What is the window's area?

• 31.25 m²
• 29.55 m²
• 30.36 m²
• 28.26 m²

Fill in the Blank

Find the circumference of the circle.

Type your answer as _____ ft

Sample: 3.14 ft

Fill in the Blank

Find the circumference of the circle.

Type your answer as _____ in

Sample: 3.14 in

Multiple Choice

What does "circumference" mean?

• Space a circle takes up
• Distance around a circle
• Line from one side of a circle to another
• Line from center of circle to side

Multiple Choice

What is the circumference of a circle with a radius of 54 m?

• 339.12 m
• 169.56 m
• 84.78 m 

Arc Length

Ex 1: Find the length of the minor arc

Multiple Choice

Find the arc length.  Leave your answer in terms of π.

• 7/4π
• 7/2π
• 1/8π
• 45π

Multiple Choice

Find the arc length of the bolded arc. Give your answer in terms of π.

• (65/12)π cm

• 17.02 cm

• (845/24)π cm

• 26π cm

Multiple Choice

In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet.  Find the measure of minor arc AB to the nearest degree.

• 90
• 60
• 55
• 113

Multiple Choice

A central angle measures $$230\degree$$ and its radius is 6 cm. What is the length of the arc intercepted by the angle? 

• 12.o4 cm

• 144.51 cm

• 24.08 cm

• 72.26 cm

Area of a Sector

Multiple Choice

Find the central angle of the sector of the circle with a radius of 12 ft, and a sector area of 72 square feet.

• $$12.75\degree$$  

• $$45\degree$$  

• $$57.30\degree$$  

• $$48.82\degree$$  

Fill in the Blank

Find the area of the sector shown. Round to the nearest hundredth

Multiple Choice

A region bounded by two radii of the circle and their intercepted arc is a ...

• arc of a circle

• sector of a circle

• arc length of a circle

• segment of a circle

Multiple Choice

What is the area of the shaded region? Round to the nearest hundredth.

• 1.26

• 452.39

• 9.42

• 113.10

Multiple Choice

What is the area of the shaded region? Round to the nearest hundredth.

• 8.38

• 2.09

• 33.49

• 14.19

Volume of Spheres

Multiple Choice

Find the volume.

• 779.6 cubic mm

• 883.6 cubic mm

• 840.6 cubic mm

• 805.9 cubic mm

Multiple Choice

What is the volume of this prism?

• 168 m³

• 280 m³

• 224 m³

• 112 m³

Multiple Select

True or false: Water is boiling at 100 degrees C.

• True

• False

Solution

Multiple Choice

Find the volume of the prism.

• 525 in²

• 525 in³

• 27 in³

• 27 in²

Multiple Choice

A cube has a height of 7 inches. What is the volume of the cube?

• 373 in.³

• 343 in.³

• 243 in.³

• 233 in.³

An ice cream cone has a height of 4 cm and a radius of 3 cm. A scoop of ice cream is placed on top of the cone in the shape of a hemisphere. If all of the ice cream melts, will the cone overflow? Show work to justify your answer.

(just pretend it is not upside down)

Example:

Multiple Choice

The volume formula of a cylinder is...

• V = πr²

• V = Bhπ

• V = Bh

• V = πh²

Multiple Choice

What is the volume of this cylinder?

• 42π in³

• 21π in³

• 63π in³

• 84π in³

Multiple Choice

How many black keys are found on a traditional piano?

• 36

• 34

• 52

• 50

Solution

Cones

Multiple Choice

Find the volume of the cone. Round your answers to the nearest tenth.

• 113.1 in³

• 37.7 in³

• 339.3 in³

Multiple Choice

Find the volume of the cone. Round your answers to the nearest tenth.

• 320.4 in³

• 314.2 in³

• 942.5 in³

• 267.4 in³

Multiple Choice

What year were the first Air Jordan's released?

• 2000

• 1970

• 1984

• 1998