Need Help In Engineering Math Question

[jayshone0]

NEED HELP URGENTLY FOR THIS PLEASE from r/SolvedMathProblems

[Buenchico]

There are quite a few maths graduates on this site but none of us are mindreaders.

What's the question?

[IJKLM]

And the odd engineering science grad, too.

Happy to help, if you post the question, as opposed to the link on your own machine.

[jayshone0]

https://www.reddit.com/r/SolvedMathProblems/comments/92el92/need_help_urgently_for_this_please/

[jayshone0]

Sorry about that

[IJKLM]

The surface area is made up of the cylindrical wall plus the circular base plus the hemispherical top.

Should be straightforward to get the first part of the question.

[New Judge]

Just the one "math" is it?

[IJKLM]

for the second part, you need touse the two equations involving A,r,h and eliminate the variable h.

then differentiate and solve for zero to get the minimum value.

Does that make sense?

[jayshone0]

A boiler tank has the form of a circular cylinder of internal radius r, topped by a hemisphere as shown below

Show that the internal surface Area, A is given as:

A=2πrh + 3πr²
and the Volume is given as:

V=πr²h + 2/3πr^3
Derive a function A = f(r) relating the value of A to the value of r for tanks with capacity (volume) 0.15m^3 .

Using the derived function, complete the table in the next slide.
(Still need to see the table on the reddit page for the rest)

[jayshone0]

Thanks man , Really just got it

[Buenchico]

I'm concerned that there appears to be typo in the question (unless it's just that my brain isn't functioning properly in this heat).

Imagine the interior of the cylinder being lined with paper and then opening that piece of paper to form a rectangle. The area of the paper will be the same as the internal area of the cylinder. It's height will be h and it's width will be the circumference of the cylinder (2πr), so the internal area of the cylinder will be 2πrh.

The internal area of the hemisphere will, unsurprisingly, be half the internal area of the full sphere (which you're told is 4πr²). So the internal area of the hemisphere must be 2πr².

Summing the two terms gives A=2πrh + 2πr² (and NOT A=2πrh + 3πr², as given in the question).

So either my brain isn't functioning properly (which is quite likely!) or there's a typo. Perhaps someone else here would care to comment?

[IJKLM]

It's all about the base, Buenchico

[fiction-factory]

Ha- good one - all about that base, 'bout that base.
Sorry, will have a look at the question shortly

[margarettom]

SA of base of cylinder = pi r squared ( sorry no maths symbols) so 3 pi r squared

[fiction-factory]

Presumably the base of the cylinder has an (internal) area of πr² Buenchico?

[IJKLM]

Which is why engineers are sometimes better than mathematicians at making things that can hold water...

[Buenchico]

Thanks, IJKLM.

I'm just being thick, as usual!

Yes, adding in the area of the base (πr²) gives
A=2πrh + 2πr² + πr² = 2πrh + 3πr²

The volume of the cylinder is equal to the area of its base (πr²) multiplied by its height (h).

The volume of the hemisphere is equal to half the volume of the full sphere.

Thus V=πr²h + 2/3πr^3

Then substitute 0.15for V and the fun really starts ;-)
(Remember that, because you're seeking A as a function solely of the radius, h needs to be regarded as a constant)

[Buenchico]

>>> Which is why engineers are sometimes better than mathematicians at making things that can hold water

I'm a pure mathematician, IJKLM. I detest it when someone comes along and actually finds a use for it!

[IJKLM]

Bloomin' engineers, eh? Always making ridiculous assumptions and guessing at things that should be properly defined.

Should be banned!

[fiction-factory]

Reminds me of the story of two professors walking past a field full of sheep. " I see the sheep have been sheared" said the engineer.
"Well certainly on the side facing us" added the mathematician.
Or something like that

[Guilbert53]

For those interested in mathematics they would love the film The man who knew infinity.

https://en.wikipedia.org/wiki/The_Man_Who_Knew_Infinity_(film)

About the mathematical genius Srinivasa Ramanujan and the prejudice he faced when he came to England.

https://en.wikipedia.org/wiki/Srinivasa_Ramanujan