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Re: volumes
Posted:
Apr 28, 1998 12:22 PM
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Terri Stone wrote:
>
> I am strugling to remember formulas and complete exercises for surface
> areas/volumes of cylinders triangles etc. Does anyone have any useful
> tips to assist and maybe some websites which have some basic exercies
> with solutions to practice with.
>
> Question:
> If a box 3cm x 3cm has a sphere inside with a radius of 1.5cm what is
> the ratio of the surface area of the sphere to the internal surface
> area of the box? I don't seem to get the correct answer
> My workings:
> SA of Box = 3*3 for side area x 6 for 6 sides = 72
> SA of sphere = 4x pi x r^2 = 4 x pi x 1.5^2 = 28.27
> therefore why is the ratio not 28:72 (7:13)? Answer as per my sheet
> is 11:21 What am I doing wrong!~! can someone take the time to help.
>
> thanks
Terri,
You have the right idea, but you need to be more careful with your
arithmetic!
(1) For the surface area of the box, 3*3*6 = 54, not 72.
(2) Note that 28:72 (which is wrong) is not the same thing as 7:13, it
is the same as 7:18, because 72/4 = 18.
(3) The surface area of the sphere simplifies to 9*PI, which is
**approximately** 28.27, so you are correct here, if you understand that
you only have an approximate answer. Then you round the 28.27 to 28
which gives you an even worse approximation.
(4) You should get the answer (11:21) from your answer sheet if you use
the approximation 22/7 for PI. The exact answer, which I would expect
from my students, is 9*PI:54, which reduces to PI:6.
As far as your more general question, I did a web search for "geometry
area formula" in Yahoo!, and found
http://www.sisweb.com/math/geometry/areasvols.htm
which looks like it has all the basic formulas you might need. You
should also be able to find these formulas in any mathematical handbook
from your local library. In the US, we have a popular series of worked
math problems called Schaum's Outlines, and I imagine there would be a
Geometry volume in the series. Such a book would give you lots of
practice problems with answers. You probably have something similar
available in Australia.
--Peter Ash
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