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#1 2013-11-03 20:31:55

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

Surface Area and Volume of Spheres, Cylinders, and Cones

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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#2 2013-11-04 01:26:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2013-11-04 03:13:04

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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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#4 2013-11-04 03:20:02

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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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#5 2013-11-04 03:27:51

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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)


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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#6 2013-11-04 03:34:19

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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?


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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#7 2013-11-04 04:08:17

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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?


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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#8 2013-11-04 04:50:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9 2013-11-04 04:54:43

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

No problem. Take all the time you need! big_smile


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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#10 2013-11-04 05:02:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

1) Correct.

2) Correct.

What did you get for 3?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#11 2013-11-04 05:05:38

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

I got (F) for #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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#12 2013-11-04 05:06:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

That is correct if you wanted the total surface area.

4) Correct.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#13 2013-11-04 05:09:10

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

4) D
5) A
6) C
7) B
8) A
9) D
10) D

I need help with 11, 12, and 13


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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#14 2013-11-04 05:13:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#15 2013-11-04 05:33:45

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

I didn't know how to do it. I'll put 5
How do I do #12 and #13


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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#16 2013-11-04 05:43:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

For 11 use this formula:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#17 2013-11-04 05:49:31

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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?


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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#18 2013-11-04 05:51:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

Those are correct! Very good.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#19 2013-11-04 05:55:30

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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?


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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#20 2013-11-04 05:57:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

Yes, those are all correct.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#21 2013-11-04 06:00:33

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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


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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#22 2013-11-04 06:02:44

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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.)


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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#23 2013-11-04 06:18:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,547

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

Hi;

For 1 and 2 use this:

where s is one side.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#24 2013-11-04 07:32:11

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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?


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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#25 2013-11-04 07:47:11

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

Re: Surface Area and Volume of Spheres, Cylinders, and Cones

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.


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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