Math help!!!?

Question

Hello if you know the volume of a object or cylinder can you determine the surface area?And if you know the surface area can you determine the volume?

Can anyone explain because i dont have the measurements just the volume or surface area so if the volume is 6 what would the surface area be?

Answer 1

Short answer: no.

Assuming you mean a solid, right circular cylinder (like a can that hasn't been opened), the volume is

V = (pi)(r^2)(h), where r is the radius and h is the height.

The surface area is

S = 2(pi)(r^2) + 2(pi)(r)(h) = 2(pi)(r)(r+h)

If you know the volume or the surface area, you get a relationship between height and radius. You need one more piece of information to complete the picture. This extra piece is commonly height, radius, or the ratio between the two.


**********************

If the volume is 6, then 6=(pi)(r^2)(h), so

h=6/[pi(r^2)]

S = 2(pi)(r)(r+h) = [2(pi)(r^3)+12]/r

...and that's the best I can do without knowing more info.

Answer 2

Actually, you can't. If you had a cylinder of almost no height, the only way to get a certain amount of volume would be to make it incredibly wide, which would produce a huge surface area (in fact, an infinitely small height would produce an infinitely large surface area). However, there are obviously cylinders that will have the same volume as the infinitely small/wide one that have finite numbers.

Conversely, knowing the surface area will not give you the volume.

Answer 3

The word object is very ambiguous. Different objects have different forms therefore they have different formulas.
For a cylinder the answer is no to both of your question. You need more measurements. You need at least either the height or radius. You must be referring to the lateral surface area?
Remember:
A = (pi)(r^2)
V = (A)(h)
c = (2)(pi)(r) = (pi)(d)
Lateral Surface Area = (2)(A) + (h)(c)
Where:
r = radius
h = height
c = circumference
d = diameter
Look at how many unknowns you are dealing with.

Answer 4

No. You could have a rectangular prism 10*20*30
V=10*20*30=6000
A=2(10*20+20*30+10*30)=2(200+600+300)=2*1100=2200

or you can have a rectangular prism 10*10*60
V=10*10*60=6000
A=2(10*10+10*60+10*60)=2(100+600+600)=2*1300=2600

Answer 5

You can know the volume of what that cylinder holds... the formula is probably in the back of your text.

And the surface area of a cylinder is there as well. Check in the glossary for your formulas.

Answer 6

yes.

volume is bh

surface is 2pi r^2 h

b=pi r2

Answer 7

yes.

Answer 8

no dear.