After you have completed your activity, you may comment on your peer's work with your name clearly stated. Be respectful of others' views.

Area of circles in diagram 1:

3.14x6.5x6.5=132.665

3.14x4.5x4.5=63.585

132.665+63.585=196.25

Area of circles in diagram 2:

3.14x3.5x3.5=38.465

3.14x7.5x7.5=176.625

176.625+38.465=215.09

The first statement is not true.

Circ. of circles in diagram 1:

3.14x13=40.82

3.14x9=28.26

40.82+28.26=69.08

Circ of circles in diagram 2:

3.14x7=21.98

3.14x15=47.1

21.98+47.1=69.08

The second statement is always true.

Diagram 1

3.14x6.5cmx6.5cm=132.665 cm2

3.14x4.5cmx4.5cm=63.585cm2

132.665cm2+63.585cm2=196.25cm2

Diagram 2

3.14x7.5cmx7.5cm=176.625cm2

3.14x3.5cmx3.5cm=38.465cm2

176.625cm2+38.465cm2=215.09 cm2

Ans:never true

Activity 2

Diagram 1

3.14x13cm=40.82cm

3.14x9cm=28.26cm

40.82cm+28.26cm=69.08cm

Diagram 2

3.14x15cm=47.1cm

3.14x7cm=21.98cm

47.1cm+21.98cm=69.08cm

Ans:Always true

Pi=3.14

White (big) = 6.5cm x6.5cm x3.14

= 132.665cm2

White (small) = 4.5cm x4.5cm

= 63.585cm2

Total (white) = 196.25cm2

Yellow (big) = 7.5cm x7.5cm

= 176.625cm2

Yellow (small) = 3.5cm x 3.5cm

= 38.465cm2

Total (yellow) = 215.09cm2

Ans: it is always false

Reason : the total of the yellow and the white circles are not the same/equal.

6.5x6.5x3.14=132.665

4.5x4.5x3.14=63.585

132.665+63.585=196.25

3.5x3.5x3.14=38.465

7.5x7.5x3.14=176.625

176.625+38.465=215.09

ans : it is never true

Area of white big circle : 3.14x6.5cmx6.5cm=132.665cm2

Area of small white circle : 3.14x4.5cmx4.5cm=63.585cm2

Sum of 2 white circles : 132.665cm2+63.585cm2=196.25 cm²

Area of big yellow circle : 3.14x7.5cmx7.5cm=176.625cm2

Area of small yellow circle : 3.14x3.5cmx3.5cm=38.465cm2

Sum of 2 yellow circles : 176.625cm2+38.465cm2=215.09 cm²

Ans : it is never true

The area of the 9cm circle is basically,

3.14x4.5x4.5=63.585cm2

The sum of area from the two white circles:

63.585+132.665=196.25cm2

The area of the 15cm circle is basically,

3.14x7.5x7.5=176.625cm2

The area of the 7cm circle is basically,

3.14x3.5x3.5=38.465cm2

The sum of area from the two yellow circles:

176.625+38.465=215.09cm2

So, as my working says, it is never true (215.09cm2 is not the same as 196.25cm2)

The first set

The small circle=6.5cmx6.5cmx3.14=132.665 cm2

The big circle=4.5cmx4.5cmx3.14=63.585cm2

Total=63.585cm2+132.665cm2=196.25 cm2

2 set

The small circle=3.5cm x3.5cmx3.14=38.465cm2

The big circle=7.5cmx7.5cmx3.14=176.625cm2

Total=176.625cm2+38.465cm2 =215.09cm2

215.09 cm2 is not equal to 196.25cm2

It is never true

1st:pi X7.5 X7.5=176.715 (Ans)

Pi X 3.5 X 3.5=38.485

176.715+38.485=215.2

2nd:pi X 4.5 X 4.5=63.617

Pi X 6.5 X 6.5=132.732

132.732+63.617=196.349 (Ans)

The answer is never true.

Diagram 1=3.14x3.5x3.5

=38.465

38.465+3.14x7.5x7.5=215.09

Diagram 2=3.14x4.5x4.5=63.585

63.585+3.14x6.5x6.5=196.25

(7x3.14)+(15x3.14)=69.08

Ans : always true

Area of set 1 (small circle): 4.5cm x 4.5cm x 3.14 = 63.585cm

Sum of areas of set 1: 132.665cm + 63.585cm =196.25cm

Area of set 2 (big circle): 7.5cm x 7.5cm x 3.14 = 176.625cm

Area of set 2 (small circle): 3.5cm x 3.5cm x 3.14 = 38.465cm

Sum or areas of set 2: 176.625cm + 38.465 =215.09cm (different answer)

Never true.

To find the circumference of the 9cm circle, we take 3.14x9=28.26

To find the 7cm circle circumference , we take 3.14x7=21.98

To find the 15cm circle circumference we take 3.14x15=47.1

40.82+28.26=69.08

21.98+47.1=69.08

In conclusion it is always true

3.14x6.5x6.5=132.665

3.14x4.5x4.5=63.585

Total area:132.665+63.585=196.25

2nd set of circles:

3.14x3.5x3.5=38.465

3.14x7.5x7.5=176.625

Total area=38.465+176.625=215.09

Ans: never true

Explanation: even though the diameters add up to the same number ,each circle has a different radius .

-Elizabeth

Diagram 1=3.14x7x3.14x15

=69.08

Diagram 2=3.14x13+3.14x9

=69.08

Small green circle->22/7x4.5x4.5=63.643

Small yellow circle->22/7x3.5x3.5=38.5

Big yellow circle->22/7x7.5x7.5=176.786

Area of circles in the first box

3.14x6.5x6.5=132.665

3.14x4.5x4.5=63.585

sum of both circles in the first box: 63.585+132.665=196.25

Area of circles in the second box:

3.14x3.5x3.5=38.465

3.14x7.5x7.5=176.625

Sum of both circles in the second box

38.465+176.625=215.09

215.09cm2 is not the same as 196.25cm2

White

3.14x3.5x3.5=38.465

3.14x7.5x7.5=176.625

176.625cm2+38.465cm2=215.09 cm2(area)

small=3.14x4.5x4.5=63.585

3.14x7.5x7.5=176.625

176.625cm2+63.585cm2=240.21cm2(area)

240.21cm2-215.09cm2=25.12cm2

The statement is never true

Explanation

13x13=169

9x9=81

169+81=250

7x7=49

15x15=225

250-225=25

Pi=3.14

White (big) = 3.14 x 13cm

= 40.82cm

White (small) = 3.14 x 9cm

= 28.26cm

Total (white) = 69.08cm

Yellow (big) = 3.14x 15cm

= 47.1cm

Yellow (small) = 3.14 x 7cm

= 21.98cm

Total (yellow) = 69.08cm

Ans: Always true

Reason: the totals of the white and yellow circles are the same.

Never true,

(3.14*6.5*6.5)+(3.14*4.5*4.5 )=196.25

(3.14*3.5*3.5)+(3.14*7.5*7.5)=215.09 (false)

(3.14*7*7)+(3.14*6*6)=266.9

(3.14*6.5*6.5)+(3.14*6.5*6.5)=265.33(false)

(3.14*9*9)+(3.14*3*3)=282.6

3.14*2*2+3.14*10*10=326.56 (false)

All of the answers do not equal to each other so i think it is never true.

Radius of small white circle=9➗2=4.5

Area of big white circle =3.14x6.5x6.5=132.665

Area of small white circle =

3.14x4.5x4.5=63.585

Total area of small circle

63.585+132.665=196.25

Radius of big yellow circle=15/2=7.5

Radius of small yellow circle=7/2=3.5

Area of big yellow circle =

3.14x7.5x7.5=176.625

Area of small yellow circle =

3.14x3.5x3.5=38.465

176.625+38.465=215.09

The difference is 215.09-196.25=18.84

The difference is:18.84cm3

Always false

15+7=22

pi X 22=69.115 (Ans)

13+9=22

pi X 22=69.115 (Ans)

The answer is always true.

Area of 13 cm circle

=3.14x6.5x6.5=132.665

Area of 9cm circle

=3.14x4.5x4.5=63.585

=63.585

Area of 7cm circle=

3.14x3.5x3.5=38.465

Area of 15cm circle=3.14x7.5x.7.5=176.625

132.665+63.585=196.25

38.465+176.625=215.09

ANS never true

Circumference of big white circle : 3.14x13cm=40.82cm

Circumference of small white circle : 3.14x9cm=28.26cm

Sum of circumference of 2 white circles : 40.82cm+28.26cm=69.08cm

Circumference of big yellow circle : 3.14x15cm=47.1cm

Circumference of small yellow circle : 3.14x7cm=21.98cm

Sum of circumference of 2 yellow circles : 47.1cm+21.98cm=69.08cm

Ans : it is always true

PI x 4.5. x 4.5=63.617 251 24

Total=132.732 289 6+63.617 251 24=196.349 540 6

PI x 3.5 x3.5=38.484 510 01

PI x 7.5 x 7.5=176.714 586 8

Total=215.199 096 8

Activity 1: Never true

Even though the total of the diameter is equal, the total area is not.

PI x 13=40.840 704 5

Pi x 9=28.274 333 88

Total=69.115 038 38

PI x 7=21.991 148 58

PI x 15=47.123 889 8

Total=69.115 038 38

Activity 2: Always true

When the total diameter is the same, the total circumference will be the same

I also used calculator PI

pi=3.14

Area of Big white circle: 3.14x6.5cmx6.5cm=132.665cm2

Area of Small white circle: 3.14x4.5cmx4.5cm=63.585cm2

Total Area of white circles: 132.665cm2+63.585cm2=196.25cm2

Area of big yellow circle: 3.14x7.5cmx7.5cm=176.625cm2

Area of small yellow circle: 3.14x3.5cmx3.5cm=38.465cm2

Total area of yellow circles: 176.625cm2+38.465cm2=215.09cm2

The total area of white circles is different from the total area of yellow circles.

I think the statement is never true.

That is because even though the total diameter is the same in both groups, we are doing pi r 2, and 3.14x3.5x3.5 is different from 3.14x7.

My reason:

For diagram 1, the green circles, the small circle’s area is 63.585(9➗2=4.5

4.5x4.5x3.14=63.585)

While the large circle’s area is 132.665( 13➗2=6.5

6.5x6.5x3.14=132.665)

Add them together: 132.665+63.585=196.25

So the sum for diagram 1 is 196.25cm2

For diagram 2, the yellow circles, the small circle’s area is 38.465 (7➗2=3.5

3.5x3.5x3.14=38.465)

The area of the large circle is 176.625(15➗2=7.5

7.5x7.5x3.14=176.625)

Add them together: 176.625+38.465=215.09cm2

They are different answers. So it is never true. You can take another number that has different diameter but same sum, when you find the area, and add the 2 circles together, still different.

i think the statement for activity 1 is (c) never true

White circle set⚪️:

Big circle area = 3.14x6.5x6.5=132.665

small circle area=3.14x4.5x4.5=63.585

total for white set is :132.665+63.585=196.25

Ans=196.25cm2

Yellow set💛:

Big circle area=3.14x7.5x7.5=176.625

Small circle area= 3.14x3.5x3.5=38.465

Total for white set is :176.625+38.465=215.09

Ans=215.09cm2

Thus it never true as the total area of both sets are not equal.

3.14x6.5x6.5=132.665

Area of small white circle:

3.14x4.5x4.5=63.585

Area of the white circles:

132.665+63.585=196.25

Area of big yellow circle:

3.14x7.5x7.5=176.625

Area of small yellow circle:

3.14x3.5x3.5=38.465

Total area of yellow circles :

176.625+38.465=215.09

Area of white circles : 196.25cm2

Area of yellow circles: 215.09

In conclusion , it will never be true

3.14x6.5x6.5=132.665cm2

9/2=4.5

3.14x4.5x4.5=63.585 cm2

63.585+132.665=196.25 cm2

7/2=3.5

3.14x3.5x3.5=38.465 cm2

15/2=7.5

3.14x7.5x7.5=176.625 cm2

176.625+38.456=215.081 cm2

Hence, it is never true :3

Radius of white circle=13/2

=6.5

Area of white circle=3.14x6.5x6.5

=132.665

Radius of yellow circle=15/2

=7.5

Area if yellow circle=3.14x7.5x7.5

=176.625

the total of yellow circle+white circle=176.625+132.665

=215.09

9/2=4.5

Area of 9cm circle=3.14x4.5x4.5

63.585

7/2=3.5

Area of 7cm circle=3.14x3.5x3.5

=38.465

Total of 7cm circle and 9cm circle

=64.585+38.465

=103.05

103.05cm2 is not equal to 215.09cm3.

Diameter of big yellow circle:

15➗2=7.5

Diameter of small yellow circle:

7➗2=3.5

Area of big yellow circle:

7.5x7.5x3.14=176.625

Area of small yellow circle:

3.5x3.5x3.14=38.465

Total area:38.465➕176.625=215.09cm2

Diameter of big white circle:13➗2=6.5

Diameter of small white circle:9➗2=4.5

Area of big white circle:6.5x6.5x3.14=132.665

Area of small white circle:4.5x4.5x3.14=63.585

Total area=132.665➕63.585=196.25 cm2

The total area of circles are not equal as there are different answers.

Area of the 13cm diameter circle=3.14x6.5x6.5

=132.665cm2

Area of the 9cm diameter circle =3.14x4.5x4.5

=63.585cm2

Area of the 7cm diameter circle =3.14x3.5x3.5

=38.465cm2

Area of the 15cm diameter circle =3.14x7.5x7.5

=176.625cm2

1st set area (13cm diameter and 9cm diameter circle)=132.665+63.585

=196.25cm2

2nd set area(15cm diameter and 7cm diameter circle)=38.465+176.625

=215.09cm2

In a nutshell, it is never true

Big white=3.14x13=40.82

Small white=3.14x9cm=28.26 cm2

40.82cm2+28.26cm2=69.08 cm²

Big yellow=3.14x7cm=21.98 cm2

Small yellow=3.14x15cm=47.1 cm2

21.98cm2+47.1cm2=69.08 cm²

69.08-69.08=0

3.14x3=9.42

3.14x17=53.38

9.42cm+53.38cm=62.8cm

diameter=20cm

3.14x10=31.4

31.4x2=62.8

62.8cm-62.8cm=0 cm

The statement always true

To find the area of the 7cm yellow circle we do 3.14x3.5x3.5=38.465

To find the area of the 15cm yellow circle we do 3.14x7.5x7.5=176.625

The total area of the yellow group would be

38.465+176.625=215.09

For the 9cm white circle area we do 4.5x4.5x3.14=63.585

For the 13cm white circle are we do

6.5x6.5x3.14=132.665

The area of the white group is 63.585cm+133.665cm=197.25cm

The total area of the two groups is clearly NOT equal so it is never true

Activity 2: I think it is always true

15cm yellow circle circumference would be

15x3.14=47.1

The 7cm yellow circle circumference would be 7x3.14=21.98

The circumference of the yellow set is

47.1+21.98=69.08

The circumference of the 13cm white circle is

13x3.14=40.82

The circumference of the 9cm white circle is

9x3.14=28.26

The circumference of the white circle set is

40.82+28.26=69.08

In conclusion for activity 2 the circumference of both sets is equal so it is always true

: 3.14x6.5x6.5=132.665

Area of the circle with diameter 9cm

: 3.14x4.5x4.5=63.585

Total:196.25cm2

Area of circle with diameter 7cm

: 3.14x3.5x3.5=38.465

Area of circle with diameter 15cm

:3.14x7.5x7.5=176.625

Total:215.09cm2

Their areas are not the same so the answer is: never true

3.14x13=40.82cm

The circumference of the 9cm circle is:

3.14x9=28.26cm

The sum of the circumferences from the white circles: 28.26+40.82=69.08

The circumference of the 15cm circle is=

3.14x15=47.1cm

The circumference of the 7cm circle is=

3.14x7=21.98cm

The sum of the circumferences from the yellow circles=47.1+21.98=69.08cm

So, as my working says, it is always true ( Both sets have the same circumference as total)

blue : 13+9=22

yellow : 7+15=22 . they are both 22 ✔️)

blue . 💙

big circle: 3.14x6.5x6.5=132.665

small circle : 3.14x4.5x4.5=63.585

total : 196.25 ( which is the sum of areas )

yellow . 💛

big circle. 3.14x7.5x7.5=176.625

small circle : 3.14x3.5x3.5=38.465

total: 215.09 ‘

so technically comparing the total of yellow + total of blue , i can conclude that it is never true .

3.14x13=40.82

3.14x9=28.26

40.82+28.26=69.08

3.14x15=47.1

3.14x7=21.98

47.1+21.98=69.08

3.14x13=40.82

3.14x9=28.26cm

Total :40.82+28.26=69.08cm

2nd set of circles:

3.14x7=21.98cm

3.14x15=47.1cm

21.98+47.1=69.08cm

ans: always true

-Elizabeth

Circumference of set 1 (Small circle): 9cm x 3.14 = 28.26cm

Sum of circumferences of set 1: 40.82cm + 28.26cm =69.08 cm

Circumference of set 2 (Big circle): 15cm x 3.14 = 47.1cm

Circumference of set 2 (small circle): 7cm x 3.14 = 21.98cm

Sum of circumferences of set 2: 47.1cm + 21.98cm =69.08 cm

Always true.

The white set ⚪️:

Small circle = 3.14x13=40.82

Big circle = 3.14 x 9=28.26

Total length = 28.26+40.82=69.08

Ans:69.08cm

The yellow set 💛:

Small circle =3.14x7=21.98

Big circle =3.14x15=47.1

Total length =47.1+21.98=69.08

Ans = 69.08 cm

In conclusion i think it is (a) always true as both total lengths are equal.

Yellow; 7.5cmx7.5cm+3.5cm+3.5c, x pi=68.5 pi cm2

White;6.5cmx6.5cm+4.5cmx4.5cmx pi=62.5 pi cm2 which is wrong because they are not the

They are never the same because a greater number while multiplied by itself would not be equivalent to a smaller number multiplied by itself.

For example

6x6+4x4 does not equal to 7x7+3x3.

Statement 2 (ALWAYS TRUE)

13cm x calculator pi + 9cm x calculator pi is equivalent to 7cm x calculator pi + 15cm x calculator pi. This is because 13cm +9cm =22cm and 7cm +15cm is also 22cm. As long as the total number of diameters from both groups is the same, and the value of pi is kept constant, the total circumference from both groups would be the same.

Always true,

13cm big circle circumference=13*3.14=40.82

Circumference of 9cm circle = 9*3.14=28.26

Sum of 13 and 9 cm circle= 28.26+40.82=69.08

Circumference of 7cm circle= 7*3.14=21.98

Circumference of 15cm circle = 15*3.14=47.1

Sum of 7 and 15 cm circle = 21.98+47.1=69.08

Ans both of the sum of circumferences are the same.

(3.14x13cm)+(3.14x9cm)=69.08cm

(3.14x7cm)+(3.14x15cm)=69.08cm

Example 2:

(3.14x15cm)+(3.14x2cm)=53.38cm

(3.14x8cm)+(3.14x9cm)=53.38 cm

3.14x13=40.82

Circumference of small white circle:

3.14x9=28.26

Circumference of big yellow circle:

3.14x15=47.1

Circumference of small yellow circle:

3.14x7=21.98

Circumference of white circles: 40.82+28.26=69.08

Circumference of yellow circles :

47.1+21.98=69.08

In conclusion, it is always true.

The area of the 13cm diameter circle is

3.14x6.5x6.5=132.665cm2

The area of the 9cm diameter circle is

3.14x4.5x4.5=63.585cm2

The area of the 7cm diameter circle is

3.14x3.5x3.5=38.465cm2

The area of the 15cm diameter circle is

3.14x7.5x7.5=176.625

Then we take 132.665cm2+63.585=196.25cm2

38.465cm2+176.625=215.09 cm²

In conclusion the answer is never true

Activity 2

The circumference of the 13cm circle is

3.14x2x6.5=40.82cm

The circumference of the 9cm circle is

3.14x2x4.5=28.26cm

The circumference of the 7cm circle is

3.14x2x3.5=21.98cm

The circumference of the 15cm circle is

3.14x2x7.5=47.1cm

Then we take

40.82cm+28.26cm=69.08 cm

21.98cm+47.1cm=69.08 cm

In conclusion the answer is that it is always true

Circumference of big yellow circle:

3.14x15=47.1

Circumference of small yellow circle:

3.14x7=21.98

Circumference of small white big circle:

3.14x13=40.82

Circumference of big white circle:

3.14x9=28.26

Total circumference of yellow circles:

47.1➕21.98=69.08

Total circumference of white circles:

40.82➕28.26=69.08

The circumference of the 2 sets of circles are always equal.

My reason: The first diagram, which is the green circles, the circumference of the small circle is 28.26(9x3.14=28.26)

The large circle’s circumference is 40.82 (13x3.14=40.82)

Add them together: 40.82+28.26=69.08cm

For diagram 2, the yellow circles, the circumference of the small circle is 21.98(7x3.14=21.98)

The area of the large circle is 47.1(15x3.14=47.1)

Add them together: 47.1+21.98=69.08cm

They both have same circumference. So it is always true.

7cm circumference-> 7x22/7=22

13cm circumference->13x22/7=40.857

15cm circumference->15x22/7=47.143

9cm circumference->9x22/7=28.286

40.857+28.286=69.143

47.143+22=69.143

Set 1

Circumference of big circle=13cmx3.14=40.82 cm

Circumference of small circle =9cm x3.14=28.26 cm

Total= 28.26cm+40.82cm=69.08cm

Set 2

Circumference of big circle=15cmx3.14=47.1cm

Circumference of small circle =7cmx3.14=21.98cm

Total=47.1cm+21.98cm=69.08 cm

The circumference of the circles in the 1 set is always the same (69.08cm)

Circumference of 13cm diameter circle =3.14x2x6.5

=40.82cm

Circumference of 9cm diameter circle =3.14x4.5x2

28.26cm

Circumference of the 7cm diameter circle =3.14x3.5x2

21.98cm

Circumference of the 15cm diameter circle =

3.14x7.5x2=47.1 cm

1st set circumference (13cm diameter circle and 9cm diameter circle)=40.82+28.26

=69.08cm

2nd set(7cm diameter circle and 15cm diameter circle)=21.98+47.1=69.08 cm

In a nutshell, it is always true

pi =3.14

Circumference of big white circle: 3.14x13cm=40.82cm

Circumference of small white circle: 3.14x9cm=28.26cm

Total circumference of white circles: 40.82cm + 28.26cm =69.08cm

Circumference of big yellow circle: 3.14x15cm=47.1cm

Circumference of small yellow: 3.14x7cm=21.98cm

Total circumference of yellow circles: 47.1cm+21.98cm=69.08cm

The circumference of both circles are the same.

The statement will always be correct.

3.14x13=40.82

3.14x9=28.26

total : 40.82+28.26=69.08 ✔️

yellow💛 :

3.14x7=21.98

3.14x15=47.1

total: 47.1+21.98=69.08 ✔️

sometimes true as it contradicts what I have worked out for activity 1 !! ._.

(3.14x7.5cmx7.5cm)+(3.14x4.5cmx4.5cm)=240.21cm

(3.14x3.5cmx3.5cm)+(3.14x7.5cmx7.5cm)=215.09cm

Example 2 (Total diameter is 20cm):

(3.14x6cmx6cm)+(3.14x4cmx4cm)=163.28cm

(3.14x7cmx7cm)+(3.14x3cmx3cm)=182.12cm