Unit 4:  Circles and Volume

A collection of books made by students and teachers at Newton County School District.

Newton County Schools

Bright ideas border

Stars pattern

Quiz: Good Luck!!! Show your work. Answers will not be accepted if the work is not shown

Find the perimeter of the triangle (4pts).

BE ABLE TO DETERMINE THE DIFFERENCE BETWEEN THE RADIUS AND THE DIAMETER

1.Identify the parts of the circle. Drag the names to the correct circle part.

2. If the radius is 10, what is the diameter?

3. If the diameter is 35, what is the radius?

You have a rectangular prism fish tank in your house.  You have a cylinder shape container to help fill the empty tank.  Once you pour the water into the fish tank.  How much of the fish tank volume is not filled with water.

RADIUS/DIAMETER AND TANGENT INTERSECT AND FORM 90 ANGLES

The candle has a volume of 25.40 cm. The candle has a height of 6 feet. Find the radius of the candle.

FIND THE VOLUME: WITHOUT PI IN THE ANSWER

FIND THE ARC LENGTH OF THE SHADED REGION.

ARC + ARC = ANGLE 2

What is the measure of minor arc AB?  (2 pts)

MGSE9-12.G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

1. FIND THE CIRCUMFERENCE OF THE CIRCLE. 2. FIND THE AREA OF THE CIRCLE. 3. FIND THE ARC LENGTH OF MINOR ARC CD. 4. FIND THE AREA OF THE SECTOR.

AB is a tangent to cIrcle O at B. Find the length of the radius r if AB=10 and AO=11.7. Round to the nearest hundredth. (4 pts).

1. WHAT IS THE MEASURE OF THE CENTRAL ANGLE? 2. WHAT IS THE MEASURE OF THE INTERCEPTED ARC? 3. WHAT IS THE MINOR ARC? 4. SOLVE FOR X.

horizontal-square/rectangle vertical-triangle

BE ABLE TO USE THE FORMULAS FOR PORTIONS OF THE CIRLCE.

1. WHAT IS THE MEASURE OF THE CENTRAL ANGLE? 2. WHAT IS THE MEASURE OF THE INTERCEPTED ARC? 3. WHAT IS THE MAJOR ARC? 4. SOLVE FOR X.

V=Bh 3 V=LWh 3

V=Bh 3 V= r h 3

V= 4 r 3

DC is tangent to circle O at point D in the picture below.&nbsp;Find the diameter of the circle if BC = 7 and DC = 19 (4 pts).

The shaded area in the circle below represents the section of the park used by the chamber of commerce for a fund-raising event. What is the approximate area of the section of the park used for the fund-raiser? (4 pts)

CROSS SECTIONS-THE 2D SHAPE YOU SEE WHEN YOU CUT THROUGH THE 3D FIGURES CAVALIERI'S PRINCIPLE-SAME HEIGHT, SAME CROSS SECTION AREA=SAME VOLUME

Find the measure of each inscribed angle and arc

BE ABLE TO SOLVE FOR X USING THE ANGLE COMPONENTS.

The central angle of a sector is 72 and the sector has an area of 50 . Find the radius. ( 4 pts)

same height same cross section area SAME VOLUME

25-10 = 2

15 =7.5 2

40-25 = 2

79-43 = 2

36 =16 2

FAR - NEAR = ANGLE 2

A sculptor chisels away at the block to make a pyramid with the same base dimensions but one-fifth the volume of the original prism. What is the height of the pyramid?

Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.&nbsp;

A frozen dinner is divided into three sections on a circular plate with a 12-inch diameter What is the approximate length of the arc of the section containing peas? (4 pts)

MGSE9-12.G.C.2 Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants.&nbsp;Include the relationship between central, inscribed and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

BE ABLE TO SOLVE FOR X USING THE SEGMENTS COMPONENTS.

Large grid paper

Find the area of the shaded region. Find the Exact Answer (pi should be in the answer). ( 4 pts)

FIND THE ARC LENGTH AND AREA OF THE SHADED REGION.

1. FIND THE CIRCUMFERENCE OF THE CIRCLE. 2. FIND THE AREA OF THE CIRCLE. 3. FIND THE ARC LENGTH OF THE MAJOR ARC AB . 4. FIND THE AREA OF THE SECTOR.

MGSE9-12.G.C.1 Understand that all circles are similar.&nbsp;

1. FIND THE CIRCUMFERENCE OF THE CIRCLE. 2. FIND THE AREA OF THE CIRCLE. 3. FIND THE ARC LENGTH OF MINOR ARC CD. 4. FIND THE AREA OF THE SECTOR.

MGSE9-12.G.GMD.1 Give informal arguments for geometric formulas. a. Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments. MGSE9-12.G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector

Find the area of the unshaded sector? Answer should be in terms of pi.

Name

Safari may block some audio or video from playing automatically and ‘read to me’ will skip these. You can configure this in Safari’s preferences.