Day 156 Bellringer Name - High School Math Teachers...15. How many quadrilaterals make up image A. 16. How many quadrilaterals make up image B. 17. Which kind of quadrilateral make

Day 156 Bellringer Name ____________________________________

HighSchoolMathTeachers@2017 Page 1

Idrntify the following images from the figures below.

1. Identify triangle(s)

2. Identify heptagon(s)

3. Identify trapezoid(s)

4. Identify rectangle(s)

5. Identify quadrilateral(s)

(i) (ii)

(iii)

(iv)

(v)

(vi)

(vii) (viii)



Answer Key

Day 156:

1. (𝑣) and (viii)

2. (vii)

3. (ii) and (iv)

4. (vi)

5. (ii), (iii), (iv) and (vi)

Day 156 Activity Name ____________________________________


1. The students will be provided with the following diagrams and asked to mold them using the

rods and clay.

2. Verify that corresponding sides of the cross section of the prism are equal

3. Verify that the length of the prism is equal for all the rectangles enclosing it



In this activity students will model polygonal prisms using plasticize (or clay) and rods (plastics,

metallic or wood). Students will work in groups of at least 4. Each group will require a sufficient

clay or plasticine, enough rods (plastics, metallic or wood cut to required sizes ready for molding

rectangular and trapezoidal based prims) and a ruler.

Answer Keys

Day 156:

1. No response

2. Different responses, the cross sections must be of the same

3. The lengths must be of the same size

Day 156 Practice Name ____________________________________


Use the following information to answer questions 1 – 8

Idenstify the number of rectangles in the following objects.

1. Cuboid

2. Cube

3. Triangular based prism

4. Parallelogram based prism

5. Pentagonal prism

6. Kite based prism

7. Rhomboid based prism

8. Hexagonal based prism




The figure below shows two 3D objects. Use then to answer the following questions.

`

9. Idetify image A

10. Identify image B

11. How many polygons that are not quadrilaterals make up image A.

12. How many polygons that are not quadrilaterals make up image B.

13. Identify the name and list the images in 11 above

B

C

D

E

F

G

Image A

K L

M

N P

Q

R S

T

U V

W

Image B



14. Identify the name and list the image in 12 bove.

15. How many quadrilaterals make up image A.

16. How many quadrilaterals make up image B.

17. Which kind of quadrilateral make up image A

18. Which kind of quadrilateral make up image B

19. List the quadrilaterals in 15 above.

20. List the quadrilaterals in 16 above.



Answer Keys

Day 156

1. 4 or 6

2. None

3. 3

4. 4

5. 5

6. 4

7. 4

8. 6

9. Triangular prism

10. Hexagonal prism

11. 2

12. 2

13. Triangles; GBF and ECD

14. Hexagons; KLMNPQ and RSTUVW

15. 3

16. 6

17. Rectangles

18. Rectangles

19. BCDF, FDEG and GEBC

20. RKLS, SLMT, TMNU, UNPV, VPQW and WQKR

Day 156 Exit Slip Name ____________________________________


Identify the number of rectangles a hexagonal based prism has.



Answer Keys

Day 156:

6




1. Identify circle(s)

2. Identify rectangle(s)

3. Identify ellipses

4. Find the perimeter of a circle whose diameter is 20 in. (write your answer in 4 significant

figures)

5. Determine the distance round a rectangle whose length is three times the width, if the width is

7 in.

(i)

(ii) (iii)

(iv)

(v)

(vi)

(vii)

(viii)



Answer Key

Day 157:

1. (iv)

2. None

3. (ii) and (vii)

4. 62.83 in

5. 56 in



1. To the cylinder provided, cut it along its length. The cut must be parallel to the length of the

cylinder.

2. The cut the top and bottom plane figures

3. Identify the name of the top and bottom plane figures. Are they equal?

4. To the other remaining figure measure all its sides as well as the interior angles.

5. Compare the length of the sides measured as well as the angles.

6. From the properties above, deduce the name of the figure.



In this activity students will demonstrate that the curved surface of a cylinder is actually a

rectangle or a square. Students will work in groups of at least 4. Each group will require a

cylindrical shaped plastic (however, it is recommended that the instructors model cylinders from

manila papers and provides them to the students), cutting tool such as a razor blade or scalpel, a

protractor and a ruler.

Answer Keys

Day 157:

1 - 2. No response

3. Circles, they are approximately equal

4. Different responses

5. Opposite length are equal

All angles are approximately equal to 90°

6. A rectangle




Identify the all object(s) whose features are listed after each statement.

1. The object has a cross section

2. The cross section is circular

3. The cross sections are not equal

4. If the cross sections were equal, what would be the object?


The figure below is cut into several parts along lines KL, LM, MN, NK and along the curved

lines. Use it to answer the following questions.

5. Identify the name of the figure above

6. What is the minimum number of plane figures can enclose the figure above?

K

L

M

N



7. Identify the plane figures in 6 above.

8. How many individual figures results when the figure above is cut as described above?

9. How many figures are recovered from the curved surface?

10. Identify the name of the figures in 9 above.

11. If the curved surface were to be a square, what would be the condition between the length

and the radius of the figure?

12. If the curved surface were to produce two squares, what would be the condition between the

length and the radius of the figure?

13. If MLKN were to be a square, what would be the relation between the radius and the height?




Draw various figures showing the curved surface when cut as described below

14. If the curved surface of the cylinder is cut from K to L using the cross section B then opened,

draw an image showing how the plane figure will look like.



K

c

a L

M

N

b

d e f





17. Identify the smallest number of geometric figures that that the image in 14 can be subdivided.

18. Identify the name of the figures in 17 above.


What would be their name?


Identify the name of these figures.



Answer Keys Day 157

1. All prisms and frustums

2. Cylinders and conical frustum

3. Conical frustum

4. Cylinder

5. Cylinder

6. 3

7. Two circles and one rectangle

8. 4

9. 2

10. Rectangles or squares

11. 𝑙 = 2𝜋𝑟

12. 𝑙 = 𝜋𝑟

13. 𝑙 = 2𝑟

14.

15.

16.

17. 2

18. A rectangle and a segment

19. 1, a rectangle

20. 3, two segments and one rectangle

a b

c d

e f



Identify if the solid drawn is a prism



Answer Keys

Day 157:

Not a prism




Identify the resultant figure in each of the following statements

1.A point on a plane is dragged through a distance about a line such that at any point in its path,

the shortest distance between the point and the line is the same.

2. A point on a plane is dragged through a distance about a fixed point such that at any point in

its path,the shortest distansce between the point on the path and the fixed point is the same.

3. A point on a space is dragged through a distance about a fixed point such that at any point in

its path, the shortest distance between the point on the path and the fixed point is the same.

4. A straight line is a plane is dragged through a distance such that the line is always

perpendicular to the direction taken.

5. What is the path described when a straight line perpendicular to the plane having a circle or

radius 𝑟 moves perpendicularly along the circle.



Answer Key

Day 158:

1. A line parallel to the first one

2. A circle whose center is the fixed point

3. A sphere whose center is the fixed point

4. A rectangle or square whose sides are the line and the length of the distance moved

5. A curved surface of the cylinder whose radius is 𝑟



1. Cut out a plane figure, for instance, a semicircle and mount it on the bar using a tape as shown

below.

2. Rotate the handle as fast as you could as well as the setup can allow. Let other students

observe from the other end as indicated.

3. Identify the image observed as the rotations are made.

4. Repeat the procedure 1 – 3 for a quarter circle and a cylinder and record the image that you

observe.

5. Make a conclusion about the resultant images with respect to the plane figures rotated.

Observer

Rotated as shown

Plane

figure

Bar

Handle



In this activity, students will try to visualize 3D images when rotated. The diagram below shows

a setup, which can be prepared by the instructor or other means then provided to students.

Students will working groups of at least six or more depending on the availability of the setup.

They will require a manila paper, a tape, and a pair of scissors or scalpel.

Answer Keys

Day 158:

1 - 2. No response

3. Sphere

4. A hemisphere and a cylinder

5. When a semicircle is rotated about a line that the diameter is part of, a sphere is observed

When a quarter circle is rotated about a line that the diameter is part of, a hemisphere is observed

When a rectangle is rotated about a line that the diameter is part of, a cylinder is observed




Identify the images the results when the following images are rotated about a line

1. A square of side 3 in; one side lies on the line of rotation

2. A square of side 5 in; one side is parallel and 1 unit from the line of rotation

3. A rectangle of side of width and length 4.5 in by 6 in respectively; a length lies on the line of

rotation

4. A rectangle of side of width and length 3 in by 5 in; a length is parallel and 1.5 in from the line

of rotation

5. A rectangle of side of width and length 3 in by 5 in; a width is parallel and 1.1 in from the line

of rotation

6. A right triangle of side of height 4 in, base 3 in and hypotenuse 5; the height lies on the line of

rotation

7. A right triangle of side of height 4 in, base 3 in and hypotenuse 5; the base lies on the line of

rotation



8. A right triangle of side of height 4 in, base 3 in and hypotenuse 5; the height is perpendicular

and touching the line of rotation


and 1.5 in from the line of rotation

10. A parallelogram; the longest side lies on the line of rotation

11. A rhombus; one side lies on the line of rotation

12 A right triangle of side of height 8 in and base 6 in; the height is perpendicular and touching

the line of rotation


and 1.5 in from the line of rotation

14. Two right triangles of side of height 4 in, base 3 in and hypotenuse 5; the triangles touch

each other at a vertex, the heights are perpendicular to the line of rotation and their bases form

one straight line.

15. A circle rotated about its tangent



16. A circle rotated about a line parallel to its tangent


Identify the surface created when line AB is rotated about line C as shown below.

17.

18.

A

B

C

A

B

C



19.

20.

A B

C

A

B

C



Answer Keys

Day 158

1. A Cylinder of radius 3 in and height 3 in

2. A cylinder of with a hollow of radius one unit and height 5 in. The outer radius of the

cylinder is 6 in

3. A cylinder of radius 4.5 in and height of 6 in

4. A hollowed cylinder of outer radius 4.5 in and a height of 5 in. The radius of the

cylindrical hole is 1.5 in

5. A hollowed cylinder of outer radius 6.1 in and a height of 3 in. The radius of the

cylindrical hole is 1.1 in

6. A cone of radius 3 in and height 4 in

7. A cone of radius 4 in and height 3 in

8. Cylinder of with a conical hollow. The height and the radius of the figure is 4 in and 3 in

respectively

9. Cylinder of with hollow of composed of a cone and a cylinder. The height is 3 in. The

radius of the cylindrical hollow is 1.5 in while that of the conical hollow is 5.5 in

10. A cylinder having a conical hollow dug from it and a comical solid added to it

11. A cylinder having a conical hollow dug from it and a comical solid added to it

12. A hollowed cylinder of radius 8 in and height 6 in. The hollow is conical in shape with a

radius of 8 in

13. A hollowed cylinder of radius 4 in and height 3 in. The hollow is composed of a cylinder

of 1.5 in radius a cone of 5.5 in.

14. A cylinder with a hollow composed of two cones whose base fused. The radius if the

cone as well as the cylinder is 4 in while the height of each cone is 3 in. The height of the

whole image is 6 in.

15. A donut(torus) with no space in between

16. A donut(torus) with a space in between

17. Curved surface of a cone

18. Curved surface of a frustum of a cone

19. Curved surface of a cylinder

20. A circle or radius AB



A square is rotated about a line that is parallel to one of the radius. Which image is formed.



Answer Keys

Day 158:

A cylinder whose height is equal to the radius



1. Which three – dimensional object is generated by rotating a circle 180° about an axis coplanar

with its diameter?

2. Which three – dimensional object is generated by rotating an equilateral triangle 180° about

an axis coplanar with its perpendicular height?

3. Which three – dimensional object is generated by rotating a rectangle 360° about an axis

coplanar with one longer side?

4. A square was rotated 180° about an axis coplanar with its diagonal. Which three –

dimensional objects were generated?

5. Which three – dimensional object is generated by rotating a semi – circle 180° about an axis

coplanar with its diameter?



Answer Key

Day 159:

1. Sphere

2. Cone

3. Cylinder

4. Two cones

5. Hemisphere


HighSchoolMathTeachers @2017 Page 35

1. On the manila paper, draw two diagrams of a rectangle with a triangle as shown.

2. Draw a line of symmetry to each diagram as shown.

3. Cut out the diagrams.

4. Apply glue on the side of the cut outs with the line of symmetry.

5. Place the wooden stick along the line of symmetry of one cut out.

6. Stick the other cut out such that the wooden stick is in between the cut outs as shown.

7. Make a hole in the card – sheet and fix a short straw to make a bearing.

8. Put the free end of the wooden stick throught the straw in the card sheet.

9. Insert a propeller on the free end of the wooden stick.

10. While holding the card – sheet, rotate the propeller and observe the shape of the cut out.

a) Which object does the rectangular part make?

b)Which object does the triangular part make?

2 𝑖𝑛

3 𝑖𝑛

2 𝑖𝑛 2 𝑖𝑛

3 𝑖𝑛

2 𝑖𝑛



In this activity, students will identify the objects generated by a rotating 2D – fused faces.

Students will work in groups of at least four and each group is required to have a pencil, a manila

paper, a simple wind propeller, glue, a razor, thick card – sheet, a 1 𝑖𝑛 straw and 8 𝑖𝑛 wooden

stick.

Answer Keys

Day 159:

1-9. No response

10. a) Cylinder

b)Cone



1. List the three dimensional objects generated by rotating the figure below about line AB.

2. The figure below is rotated 360° about line CD.

Which three – dimensional objects are generated by the rotation?

3. The figure below is rotated 180° about its line of symmetry. State the three-dimensional

objects generated by the rotation.

B

A

C

D E

F

G

H



4. Which three – dimensional objects are generated by rotating the figure below 360° about line

HI?

5. Identify all three – dimensional objects generated when the figure below is rotated 180° about

line JK.

6. Which 3D objects are generated by rotating the figure below about line LM?

7. Identify 3D objects generated by rotating the figure given below about line AB.

H

I J

K

J K

L M

A B



8. The figure below was rotated 180° about line PR. Identify three – dimensional objects that

were generated.

9. The figure below was rotated 180° about line QR. Identify three – dimensional objects that

were generated.

10. The figure below was rotated 180° about line MN. Identify three – dimensional objects that

were generated.

Use the figure below to answer questions 11 – 14.

The figure was rotated 180° about line AB.

11. Identify three – dimensional object generated by FHIJ.

P R

Q R

A

B

A B

C D

E

F H

I

K

J M L



12. Identify three – dimensional object generated by EFJK.

13. Identify three – dimensional object generated by DEKL.

14. Identify three – dimensional object generated by CDLM.


The figure was rotated 180° about line SQ.

15. Identify three – dimensional object generated by ABHI.

16. Identify three – dimensional object generated by BCGH.

17. Identify three – dimensional object generated by CDFG.

18. Identify three – dimensional object generated by DEF.

A B

C D

E

F G

H I

S Q




The figure was rotated 180° about line MN.

19. How many frustums are generated by the rotation?

20. How many cylinders are generated by the rotation?

M N



Answer Key

Day 159:

1. A cylinder and a truncated sphere.

2. Two cylinders and a frustum

3. A sphere and two cylinders

4. A sphere a cone and a cylinder

5. A cone, a frustum and a cylinder

6. Two cones and a cylinder

7. A cylinder with hemispheres at both ends

8. Two cones at both ends and a cylinder at the center

9. A cone and two cylinders

10. A sphere with a conical hole

11. Cylinder

12. Frustum

13. Frustum

14. Cylinder

15. Cylinder

16. frustum

17. Cylinder

18. Cone

19. 3

20. 1



Which three – dimensional objects are generated if the figure below is rotated 360° about axis

coplanar with line AB.

A

B C

D



Answer Keys

Day 159:

A cylinder with an hemisphere at the top.

Day 156 Bellringer Name - High School Math Teachers...15. How many quadrilaterals make up image A. 16. How many quadrilaterals make up image B. 17. Which kind of quadrilateral make

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