Question

a close cylindrical tank has a capacity of 576.56 cu. m. what must the minimum surface area of the tank?

a. 412. 60 cu. m.
b 383. 40 cu. m.
c 516. 32 cu. m.
d 218. 60 cu. m.

Answer 1

First you need formulae for the volume and surface area of a cylinder:
http://math.about.com/od/formulas/ss/surfaceareavol_3.htm

First, why are the answers all in cubic metres? Surface area should be in metres squared.

Answer 2

i dont know y im nose bleed in english hahaha

Answer 3

v=pi*r^2 h
diff it
get
dh/dr
then diff the surface area replace dr to dh
using equation from vol and
then equate with 0
get r/h
get answer

Answer 4

any problem in the given theory

Answer 5

Ah well, i'm guessing they're meant to be sq cm. From the volume formula, we can get either r in terms of h, or h in terms of r. h in terms of r is probably easier, given the SA equation.

\[V= 576.56 = \pi r ^{2}h \]
\[h = \frac{ V }{ \pi r ^{2} }\]
Now put that into the surface area equation and simplify a bit:
\[SA = 2\pi r ^{2}+\frac{ 2V }{ r }\]
Then differentiate and set SA' = 0.

Answer 6

ano po yun answer?

Answer 7

\[SA' = 0 = 4\pi r - \frac{ 2V }{ r ^{2}}\]
rearrange for r:
\[r = \sqrt[3]{\frac{ V }{ 2\pi }} \]
so r = 4.51
and now sub that into your SA equation.