Word Problem

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alyren

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Sep 9, 2010
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A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. the top and bottom are made up of a material that costs 8 cent per square centimeter, while the sides are made of material that costs 5 cents per square centimeter. find a function that describes the total cost of the material as a function of the radius r of the cylinder.

need help to set up the equation.
 
alyren said:
A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. the top and bottom are made up of a material that costs 8 cent per square centimeter, while the sides are made of material that costs 5 cents per square centimeter. find a function that describes the total cost of the material as a function of the radius r of the cylinder.

need help to set up the equation.
Click to expand...
The first step in setting up equations - is to define variables.

What are your variables?

Please show us your work indicating exactly where you are stuck - so that we may know where to begin to help you.
 
so far this is what i gotten

Volume of cubic cylinder = pi x r^2 multiplied by the height of the cylinder.
So pi x r^2 x h = 700 cm^3
Circumference of circle = pi x diameter
Solve for h: h= 700 cm^3 / pi X diameter
Cost of material =
- Top and bottom: 2(pi x r^2) x 8 cents
- Sides: Circumference x height x 5 cents
2(pi x r^2) x 8 cents + (pi x r^2)(700 cm^3) / (pi x diameter) x 5 cents

is there any step i missed or doing wrong?
 
Since you gave an earnest effort.

You need the area of the circle, not the circumference.

The volume is

\(\displaystyle {\pi}r^{2}h=700\)

Solve for h:

\(\displaystyle h=\frac{700}{{\pi}r^{2}}\)

Sub into the formula for surface area of a cylinder:

\(\displaystyle S=\frac{1}{20}\cdot 2{\pi}r\left(\frac{700}{{\pi}r^{2}}\right)+\frac{2}{25}\cdot 2{\pi}r^{2}\)

Now, simplify.

I used fractions for the cents instead of decimals. Looks nicer. I think so anyway.
 
is this right? S=0.1 pi r(700/pi r^2)+0.16pi r^2, do i need to turn that pi into 3.14?
 
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