Posted by **Mackenzie** on Monday, February 4, 2008 at 8:03pm.

what should be the dimensions of the cylinder if you wanted it to have the least amout of surface area as possible?

the cylinders volume is 100ft cubed

- math -
**bobpursley**, Monday, February 4, 2008 at 8:06pm
I assume this is calculus class.

Volume= PI*radius^2*h

h= volume/(PI*radius^2)

Surface=PI*radius^2*2 + PI*radius*height

Surface= PI*radius^2 * 2 + PI*radius*volume/(PI*radius^2)

Take the derivative of surface with respect to radius, set it to zero, and solve for radius.

- math -
**Mackenzie**, Monday, February 4, 2008 at 8:08pm
i am only in 7th grade! Could you explain that a little more to me

- math -
**bobpursley**, Monday, February 4, 2008 at 8:13pm
Sorry, this question is a typical college level calculus question. For a seventh grader, it is a little harder.

Try this. Graph Surface area vs radius according to the equation I gave you...

Surface= 2*PI*radius^2 + 100/radius

You will see a graph that has a minimum. If you have a graphing calculator, it is easy to graph.

Once you have the minimum, read the radius point on the curve. Then,

Height= 100/(PI*radius^2)

This problem is a bit advanced for a seventh grader.

- math -
**bobpursley**, Monday, February 4, 2008 at 8:27pm
I dont get that. I get the diameter to be 5.84 feet (twice the cube root of 25).

You can figure the height . I get less than four feet.

check me.

- math -
**bobpursley**, Monday, February 4, 2008 at 8:31pm
One note. I included the ends in the surface area. If they are not to be included, then it is a different answer.

- math -
**Mackenzie**, Monday, February 4, 2008 at 8:33pm
what ends?

## Answer this Question

## Related Questions

- MATH - what should be the dimensions of the cylinder if you wanted it to have ...
- Geometry - what are the dimensions of two cylinders where the first cylinder has...
- Pre Algabra - If there is a cylinder that has a volume of 100 ft, what would be ...
- maths - two cylinders have identical bases with differnt lengths.the length of ...
- math-PLEASE CHECK AND HELP - find the surface area and volume of the right ...
- calculus - An oil can is to be made in the form of a right circular cylinder to ...
- Math - A rectangular prism has a length of 100 cm, a height of 10 cm and a ...
- Math - Optimization Problem A right circular cylindrical can of volume 128tπ...
- Math help - Good Evening If i have a cylinder that has the volume of 141cm cubed...
- physics - If the aim is to let a 700 kg pump float on the surface of water, how...

More Related Questions