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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

Hi,

Could you help me with this lesson. Any help is appreciated.

Thank you!

What is surface area and volume of the given shape, if the radius is 6, the height is 8, and the slant height is 10. (Not all shapes will require all three numbers.)

1. surface area of the sphere

A 144*pi

B 324*pi

C 456*pi

D 160*pi

E 173*pi

F 297*pi

2. volume of the sphere

A 214*pi

B 288*pi

C 165*pi

D 489*pi

E 346*pi

F 228*pi

3. surface area of the cylinder

A 654*pi

B 184*pi

C 124*pi

D 656*pi

E 247*pi

F 168*pi

4. volume of the cylinder

A 537*pi

B 987*pi

C 478*pi

D 288*pi

E 576*pi

F 454*pi

5. surface area of the cone

A 96*pi

B 78*pi

C 45*pi

D 24*pi

E 33pi

F 36*pi

6. volume of the cone

A 65*pi

B 46*pi

C 96*pi

D 32*pi

E 44*pi

F 28*pi

What is surface area and volume of the given shape, if the radius is 12, the height is 16. (Not all shapes will require both numbers.)

7. surface area of the sphere

A 196*pi

B 576*pi

C 248*pi

D 493*pi

E 165*pi

F 346*pi

8. volume of the sphere

A 2304*pi

B 2491*pi

C 3780*pi

D 1258*pi

E 2560*pi

F 5145*pi

9. surface area of the cylinder

A 345*pi

B 159*pi

C 781*pi

D 672*pi

E 248*pi

F 489*pi

10. volume of the cylinder

A 2485*pi

B 1964*pi

C 2501*pi

D 2304*pi

E 5499*pi

F 1059*pi

11. What would the slant height of the cone be?

A 54

B 16

C 35

D 12

E 20

F 91

12. surface area of the cone (with the slant height from # 11)

A 159*pi

B 215*pi

C 621*pi

D 384*pi

E 126*pi

F 336*pi

13. volume of the cone

A 158*pi

B 268*pi

C 558*pi

D 255*pi

E 768*pi

F 189*pi

What is surface area and volume of the given shape, if the radius is 9, the height is 12. (Not all shapes will require both numbers.)

14. surface area of the sphere

A 324*pi

B 485*pi

C 312*pi

D 943*pi

E 652*pi

F 645*pi

15. volume of the sphere

A 841*pi

B 126*pi

C 423*pi

D 146*pi

E 479*pi

F 972*pi

16. surface area of the cylinder

A 458*pi

B 145*pi

C 540*pi

D 378*pi

E 405*pi

F 942*pi

17. volume of the cylinder

A 844*pi

B 145*pi

C 548*pi

D 879*pi

E 972*pi

F 655*pi

18. What would the slant height of the cone be?

A 15

B 95

C 24

D 18

E 36

F 27

19. surface area of the cone (with the slant height from # 18)

A 844*pi

B 216*pi

C 469*pi

D 881*pi

E 198*pi

F 112*pi

20. volume of the cone

A 910*pi

B 523*pi

C 128*pi

D 294*pi

E 341*pi

F 324*pi

I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.

-Roger Waters

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,194

Hi;

Those you do in the same way as in the other thread we went over.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

1. area = 4 * pi * r^2

area = 4 * pi * 6^2

area = 4 * pi * 36

area = 144pi

What are the two formulas for number 2 and 3?

I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.

-Roger Waters

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

Oh wait I got it. Volume of sphere = (4/3)(PI)r^3

and

surface area of cylinder is T = 2(PI)rh + 2(PI)r^2

cylinder volume is V = (PI)(r^2)h

I'll do numbers 2, 3, 4 and post them now.

I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.

-Roger Waters

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

2. V = (4/3)(PI)r^3

v= (4/3) * pi * 216

v = 288pi (B)

3. T = 2(PI)rh + 2(PI)r^2

t = 2 * pi * 48 + 2(pi) * 6^2

t = 2 * pi * 48 + 2pi * 36

What next?

4. V = (PI)(r^2)h

v = pi * 6^2 * 8

v = pi * 36 * 8

v = pi * 288

v = 288pi (D)

-Roger Waters

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

5. Surface area of cone

T = (PI)rs + (PI)r^2

t = pi * 6 * 10 + pi * 6^2

t = 60pi + 36pi

t = 96pi (A)

6. Volume of the cone

V = (1/3)(PI)(r^2)h

v = (1/3) * pi * 6^2 * 8

v = 1/3 * pi * 36 * 8

v = 96pi (C)

I also think I figured out the next step for number 3

T = 2(PI)rh + 2(PI)r^2

t = 2 * pi * 48 + 2(pi) * 6^2

t = 2 * pi * 48 + 2pi * 36

t = 96pi + 36 *2pi

Then what?

-Roger Waters

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

7. surface area of the sphere

4 * pi * r^2

a = 4 * pi * 12^2

a = 144pi * 4

a = 576pi (B)

8. volume of the sphere

V = (4/3)(PI)r^3

v= 4/3 * pi * 12^3

v= 4/3 * pi * 1728

v = 2304pi (A)

9. surface area of the cylinder

T = 2(PI)rh + 2(PI)r^2

t = 2 * pi * 192 + 2pi * 144

t = 384pi + 144 * 2pi

What do I do now?

10. volume of the cylinder

V = (PI)(r^2)h

v = pi * 12^2 * 16

v = pi* 144 * 16

v = 2304pi (D)

Sorry for all these posts!

I got 3 and 9

3 is (F) and 9 is (D).

14. surface area of the sphere

4 * pi * r^2

4 * pi * 9^2

4 * pi * 81

= 324pi (A)

15. volume of the sphere

V = (4/3)(PI)r^3

v = 4/3 * pi * 9^3

v = 4/3 * pi * 729

v = 972pi

16. surface area of the cylinder

T = 2(PI)rh + 2(PI)r^2

t = 2 * pi * 108 + 2 * pi * 81

t = 216pi + 162pi

t = 378pi (D)

17. volume of the cylinder

V = (PI)(r^2)h

v = pi * 9^2 * 12

v =pi * 81 * 12

v = 972pi (E)

Okay so I need help with 11, 12, 13, 18, 19, 20.

Are those all correct now till now?

-Roger Waters

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,194

Hold on please I just got up, will need some time to check.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

No problem. Take all the time you need!

-Roger Waters

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,194

1) Correct.

2) Correct.

What did you get for 3?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

I got (F) for #3

-Roger Waters

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,194

That is correct if you wanted the total surface area.

4) Correct.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

4) D

5) A

6) C

7) B

8) A

9) D

10) D

I need help with 11, 12, and 13

-Roger Waters

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,194

Hold on, I am still checking:

5) Correct.

6) Correct.

7) Correct.

8) Correct.

9) Correct.

10) Correct.

For 11 I got E, what did you get?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

I didn't know how to do it. I'll put 5

How do I do #12 and #13

-Roger Waters

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,194

For 11 use this formula:

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

11. sqrt of (16^2 + 12^2)

= sqrt of (256 + 144)

= sqrt of 400

= 20 (E) Alright!!

12. Surface area of cone

T = (PI)rs + (PI)r^2

t = pi * 12 * 20 + pi * 144

t = 240pi + 144pi

t = 384pi (D)

13. Volume of the cone

V = (1/3)(PI)(r^2)h

v = (1/3) * pi * 144 * 16

v = (1/3) * pi * 2304

v = 1/3 * 2304pi

v = 768pi (E)

Are those correct?

-Roger Waters

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,194

Those are correct! Very good.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

18. What would the slant height of the cone be?

sqrt of (r^2 + h^2)

sqrt of (81 + 144)

sqrt of 225

= 15 (A)

19. Surface area of cone

T = (PI)rs + (PI)r^2

t = pi * 9 * 15 + pi * 9^2

t = pi * 135 + pi * 81

t = 135pi + 81pi

t = 216pi (B)

20. Volume of the cone

V = (1/3)(PI)(r^2)h

v = (1/3) * pi * 9^2 * 12

v = (1/3) * pi * 81 * 12

v = (1/3) * 972pi

v = 324pi (F)

Good?

-Roger Waters

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,194

Yes, those are all correct.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

I sent them in and got 20/20 B) Thanks! I need help with some questions from the next lesson.

-Roger Waters

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

1. If a hexagon has a side of 3 units, what is the area of the hexagon?

2. If a hexagon has an area of 100 units, what is the length of one side?

3. If a hexagon has a radius (center to point of angle) of 6, what is the side of the hexagon?

4. If a hexagon has a radius (center to point of angle) of 6, what is the area of the hexagon?

5. If a hexagon is resting on a flat side, and has a total height of 18, what is the length of each side of the hexagon?

6. If a hexagon is resting on a flat side, and has a total height of 18, what is the area of the hexagon?

7. Problem solver (worth 4 points): Come up with a way to find the area and volume of a football. Include in your answer a way to acquire any necessary measurements without cutting or otherwise destroying the football. Also include all necessary formulas to implement your idea. (You don't need to find actual numbers, just outline the method in step by step detail--think of all the measurements you'll need to acquire and how you'll get them.)

-Roger Waters

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,194

Hi;

For 1 and 2 use this:

where s is one side.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

So

1. area = 1/2 (3sqrt3) * s^2

area = 1/2 (3sqrt3) * 3^2

area = 1/2 (3sqrt3) * 9

What next?

I looked up a little bit online and found out that this formula should be used

s^2 x 6 / 4 x tan(180/6)

Is that also correct?

-Roger Waters

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**rogerwaters****Member**- Registered: 2013-11-02
- Posts: 85

1. If a hexagon has a side of 3 units, what is the area of the hexagon?

area = 3^2 x 6 / 4 x tan(180/6)

area = 54 / 4 x tan(180/6)

area = 54 / 2.3094

area = 23.38

or

area = 1/2 (3sqrt3) * s^2

area = 1/2 (3sqrt3) * 3^2

area = 1/2 (3sqrt3) * 9

area = 23.38

2. If a hexagon has an area of 100 units, what is the length of one side?

100= 3√3 / 2 * s² | s = side

s^2 = 100 / 3√3 / 2

s^2 = 100 / 2.598076

s^2 = 38.490021

Answer: s = 6.204032

But the formula you recommended does not lead to the same result.

-Roger Waters

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