Question

A cylinder has a radius of 12 m and a height of 9 m. What is the exact volume of the cylinder?

Answer 1

\[v=\pi r^2 h\]
Plug in the numbers, leave \(\pi\) as a symbol

Answer 2

1296? pie squared

Answer 3

4069.44

Answer 4

@Mr.Man420 That's not an exact value, because \(\pi\) has an unending set of digits, so multiplying it with an integer (such as 12*12*9) must also give an unending set of digits.

Answer 5

\(\pi\) is the Greek letter "pi", not "pie" :-)

How are you getting \(\pi^2\) in your answer?

Answer 6

lol

Answer 7

\[V = \pi r^2h = \pi (12\text{ m})^2(9\text{ m}) = \pi * 12*12*9 \text{ m}^3 =\]

Answer 8

so how could you get an exact answer if its unending?

Answer 9

By leaving \(\pi\) as a symbol. \(3\pi\) is an exact quantity. You just can't write down a string of digits that expresses it exactly.

Answer 10

closest estimation is 3.14

Answer 11

No, that's not the closest estimation. That's about the least closest estimation :-)

Answer 12

:p

Answer 13

Here's a closer estimation, for example:
\(\pi \approx \)3.14159265358979323846264338327950288419716939937510582097494459230781\
6406286208998628034825342117067982148086513282306647093844609550582231\
7253594081284811174502841027019385211055596446229489549303819644288109\
7566593344612847564823378678316527120190914564856692346034861045432664\
8213393607260249141273724587006606315588174881520920962829254091715364\
3678925903600113305305488204665213841469519415116094330572703657595919\
5309218611738193261179310511854807446237996274956735188575272489122793\
8183011949129833673362440656643086021394946395224737190702179860943702\
7705392171762931767523846748184676694051320005681271452635608277857713\
4275778960917363717872146844090122495343014654958537105079227968925892\
3542019956112129021960864034418159813629774771309960518707211349999998\
3729780499510597317328160963185950244594553469083026425223082533446850\
3526193118817101000313783875288658753320838142061717766914730359825349\
0428755468731159562863882353787593751957781857780532171226806613001927\
876611195909216420199

Answer 14

What is the exact volume of the cylinder?

Answer 15

Math, so confuseing...

Answer 16

@.WhiteDragon. haven't seen your correct answer for the original problem yet...

Answer 17

1296m pi squared

Answer 18

You said that already. That isn't correct.

Answer 19

What is the exact volume of the cylinder?

Answer 20

\[V = \pi r^2h = \pi (12\text{ m})^2(9\text{ m}) = \pi * 12*12*9 \text{ m}^3 =\]

Answer 21

well then what is it

Answer 22

1296 pi m squared

Answer 23

No. Why do you keep saying that? How do you multiply \[\large\pi*12*12*9 \text{ m}^3 \]and get the answer you keep supplying?

Answer 24

Is \(\pi\) being squared anywhere?

Answer 25

Units of volume have dimensions \[\text{[length]}^3\]so the units are incorrect as well

Answer 26

well then help

Answer 27

All you have to do is carefully and correctly multiply the quantities I put in front of you. You keep saying "squared" — what is making you think that you should say that?

Answer 28

Here's a hint:

If you have a square with sides \(3\text{ m}\), the area is given by \[A = s^2 = (3\text{ m})(3\text{ m}) = 3*3*\text{m}*\text{m} = 9\text{ m}^2\]

If you have a cube with sides of the same length, the volume is given by \[V = s^3 = (3\text{ m})(3\text{ m})(3\text{ m}) = 3*3*3*\text{m}*\text{m}*\text{m} = 27\text{ m}^3\]

The units are not plucked out of the air — they are a direct result and part of the calculation. If you have the wrong units, you may well have made additional mistakes elsewhere in the calculation. That's one of the reasons why understanding how to use and manipulate units is important.