Using fixed volume to find minimum surface area of cylindrical container w/ hemispherical lid, flat base

[briscoecharles1]

"A cylindrical container is fabricated from sheet metal. The container is required to have a hemispherical lid and a flat base and have a capacity of 280000 L. Determine the minimum surface area of sheet metal required to make this container."
So what I have so far is that the volume of the container is 280m^3, But I can't understand what to do from here. Any help would be greatly appreciated.

 

[stapel]

"A cylindrical container is fabricated from sheet metal. The container is required to have a hemispherical lid and a flat base and have a capacity of 280000 L. Determine the minimum surface area of sheet metal required to make this container."
So what I have so far is that the volume of the container is 280m^3, But I can't understand what to do from here. Any help would be greatly appreciated.

(a) What is the formula for the lateral surface area of a right circular cylinder with height [imath]h[/imath] and radius [imath]r[/imath]?

(b) What is the formula for the surface area of half of a sphere with the same radius [imath]r[/imath]?

(c) What is the formula for the area of the circle with radius [imath]r[/imath], which forms the base?

(d) What then is the formula for the total surface area of the container?

(e) What is the formula for the volume of a right circular cylinder with height [imath]h[/imath] and radius [imath]r[/imath]?

(f) What is the formula for the volume of half of a sphere with the same radius [imath]r[/imath]?

(g) What then is the formula for the total volume of the container?

(h) What is the given value of the volume of the container?

(i) For which of the two variables have you chosen to solve the volume equation?

(j) What do you get when you plug the result into the surface-area equation, and minimize?

Please reply showing all of your work. Thank you!

Eliz.

 

[khansaheb]

"A cylindrical container is fabricated from sheet metal. The container is required to have a hemispherical lid and a flat base and have a capacity of 280000 L. Determine the minimum surface area of sheet metal required to make this container."
So what I have so far is that the volume of the container is 280m^3, But I can't understand what to do from here. Any help would be greatly appreciated.

That should be:

the minimum volume of the container is 280m^3................ important fact to remember while rounding up/down your answer

 

[Dr.Peterson]

"A cylindrical container is fabricated from sheet metal. The container is required to have a hemispherical lid and a flat base and have a capacity of 280000 L. Determine the minimum surface area of sheet metal required to make this container."
So what I have so far is that the volume of the container is 280m^3, But I can't understand what to do from here. Any help would be greatly appreciated.

I'm curious about the problem. How do you fabricate a hemisphere from (flat) sheet metal, and does that process change its area? Or is the lid considered to be separate from the container, so its area doesn't count?