Surface Area and Volume of Spheres, Cylinders, and Cones

rogerwaters · 2013-11-03 20:31:55

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

bobbym · 2013-11-04 01:26:13

Hi;

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

rogerwaters · 2013-11-04 03:13:04

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?

rogerwaters · 2013-11-04 03:20:02

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.

rogerwaters · 2013-11-04 03:27:51

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)

rogerwaters · 2013-11-04 03:34:19

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?

rogerwaters · 2013-11-04 04:08:17

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?

bobbym · 2013-11-04 04:50:47

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

rogerwaters · 2013-11-04 04:54:43

No problem. Take all the time you need!

bobbym · 2013-11-04 05:02:37

1) Correct.

2) Correct.

What did you get for 3?

rogerwaters · 2013-11-04 05:05:38

I got (F) for #3

bobbym · 2013-11-04 05:06:30

That is correct if you wanted the total surface area.

4) Correct.

rogerwaters · 2013-11-04 05:09:10

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

I need help with 11, 12, and 13

bobbym · 2013-11-04 05:13:47

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?

rogerwaters · 2013-11-04 05:33:45

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

bobbym · 2013-11-04 05:43:12

For 11 use this formula:

rogerwaters · 2013-11-04 05:49:31

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?

bobbym · 2013-11-04 05:51:09

Those are correct! Very good.

rogerwaters · 2013-11-04 05:55:30

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?

bobbym · 2013-11-04 05:57:53

Yes, those are all correct.

rogerwaters · 2013-11-04 06:00:33

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

rogerwaters · 2013-11-04 06:02:44

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.)

bobbym · 2013-11-04 06:18:18

Hi;

For 1 and 2 use this:

where s is one side.

rogerwaters · 2013-11-04 07:32:11

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?

rogerwaters · 2013-11-04 07:47:11

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.

Math Is Fun Forum

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

Surface Area and Volume of Spheres, Cylinders, and Cones

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

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

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

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

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

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

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

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

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

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

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