# calculus

posted by .

An open-topped cylindrical pot is to have volume 125 cm3. Determine the minimum possible amount of material used in making this pot? Neglect the thickness of the material as well as possible wastage. Give your answer accurate to 2 decimal places

• calculus -

In other words determine the minimum surface area for the given volume.

V = pi r^2 h
so h = 125/(pi r^2)

A = pi r^2 + 2 pi r h

A = pi r^2 + 2 pi r(125/(pi r^2))
A= pi r^2 + 250/r
dA/dr = 0 at min = 2 pi r -250/r^2

so
2 pi r = 250/r^2
pi r^3 =125
pi^(1/3) r = 5
r = 5/pi^(1/3)

## Similar Questions

1. ### Calculus

The radius of a tank can not exceed 5m, and the height can not exceed 12 m. Is it possible to construct a tank with a volume of 900m^3?
2. ### calculus

A box with a square base and an open top is to have a volume of 68in^3 . Neglect the thickness of the material used to make the box, and find the dimensions of the box that would minimize the amount of material used. The width and …
3. ### Calculus

An open-topped cylindrical pot is to have volume 125 cm3. Determine the minimum possible amount of material used in making this pot?
4. ### calculus

an open topped cylingrical pot is to have a volume of 125 cm^3. determine the minimal possible amount of material used in making this pot.( neglect the thickness of the material as well as possible waste)
5. ### calculus

An oil can is to have a volume 1000in^3 and is to be shaped like a sylinder with a flat bottom but capped by a hemisphere. Neglect the thickness of the material of the can and find the dimensions that will minimize the total amount …
6. ### Calculus

an open topped cylinder has a volume of 125 cubic inches. determine the radius of the pot that will minimize it's surface area. What I have so far... radius =r keight =h V=πr²h 125/πr²=h SA = πr² + 2πr(h) = πr² …
7. ### calculus

Imagine making a tent in the shape of a right prism whose cross-section is an equilateral triangle (the door is on one of the triangular ends). Assume we want the volume to be 2.2 m3, to sleep two or three people. The floor of the …
8. ### calculus help

A drinking cup is made in the shape of a right circular cylinder. for a fixed volume, we wish to make the total material used, the circular bottom and the cylindrical side, as small as possible. Find the ratio of the height to the …
9. ### calculus help

A drinking cup is made in the shape of a right circular cylinder. for a fixed volume, we wish to make the total material used, the circular bottom and the cylindrical side, as small as possible. Find the ratio of the height to the …
10. ### Calculus

Imagine making a tent in the shape of a right prism whose cross-section is an equilateral triangle (the door is on one of the triangular ends). Assume we want the volume to be 2.2 m3, to sleep two or three people. The floor of the …

More Similar Questions