Question

A cylindrical boiler is to have volume of 1.340 cu. ft. The cost of the metal sheets to make boiler should be minimum.what should be its base diameter?
a. 7.08ft
b. 10.95ft
c. 8.08.ft
d. 11.95ft

Answer 1

boiler means its open at the top?

Answer 2

i dont know i find it on google http://www.google.com.ph/search?q=cylindrical+boiler+example&hl=tl&prmd=imvnsb&source=lnms&tbm=isch&ei=DiiET_qONo6aiQfa7aXmBw&sa=X&oi=mode_link&ct=mode&cd=2&ved=0CA4Q_AUoAQ&biw=1152&bih=77

Answer 3

diameter of the base should be equal to the height

Answer 4

"boiler" in this case just means cylinder

Answer 5

The idea is the same as for the rectangular box problem. But you use slightly different equations.

You need the formula for the surface area of a cylinder (with a top and bottom), and the formula for the volume of a cylinder. Google always works if you don't know these.

\( A= 2 \pi r^2 + 2\pi r h\)
\( V= \pi r^2 h \)

Answer 6

interesting to minimize surface area i get diameter should be about 1.19
but thats not one of the choices

Answer 7

Every boiler I've ever seen has both a top and bottom ( a containment for water), used to create steam and heat a house. There is one near where I live, that is used to heat pallets.

Answer 8

this is what i hate from my prof if the answer is not in the choices we Put E

Answer 9

hmm are you sure d) isn't off by a decimal ?

Answer 10

11.95 yup

Answer 11

if i imagine a boiler i feel the diameter is around 7ft up

Answer 12

http://ce-review.com/category/mathematics_surveying_transportation/mathematics-surveying-and-trasportation-engineering/ my question is the same here but im a i.t student not a civil engineer

Answer 13

In that case, 1.340 cu. ft. should read 1340 cu. ft.

If we use this (new and improved) value, we get one of your choices.

Answer 14

yah in my prof question 1.340 but in the site question its 1340 LOL

Answer 15

Can you solve the problem?

Start with
\[ V= \pi r^2 h \]
and solve for h in terms of V and r
put this expression for h into
\[ A= 2 \pi r^2 + 2\pi r h \]
now take the derivative wrt r, set to 0 and solve for r
double r to find d

Answer 16

i cant solve this 1 honestly

Answer 17

ahh i had a feeling it had to be d)
yeah i was using 1.34

Answer 18

can i tell my prof the question is wrong? not accurate?
what do you think?

Answer 19

=)

Answer 20

no its just a typo, answer is clearly 11.95

Answer 21

I would solve it using 1340, and say that otherwise none of the choices match

Answer 22

The real point is learning how to solve these problems, and then showing people that you can do it.

Answer 23

@phi, Would you put h in terms of R?

Answer 24

\[V \over r ^{2}\pi\]

Answer 25

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

Answer 26

Thanks.

Answer 27

yes, where V is a known constant.

Answer 28

In this case the volume is given, but, we are unsure of the accuracy. or veracity???

Answer 29

The volume as given (1.34 cu. ft.) is inconsistent with any of the diameters given as a choice. Dumbcow found d= 1.19 ft. But if we use 1340 (matches the problem steph posted above) we can match with answer d

Answer 30

O.K. HooRay for dumbcow!!

Answer 31

Maybe the . in 1.340 should be a comma 1,340. Who knows?

Answer 32

You are probably correct, a typo

Answer 33

i will punish my prof on thursday dont worry =)

Answer 34

Joke

Answer 35

The question remains: Steph, can you solve this problem?

Answer 36

waaa

Answer 37

phi when my prof giving this test homework he always smile to all the student u know y? because he knows we dont know this =) but where working hard to find the answer..

Answer 38

hey step are prof are the same when i check your question here i find that the question is wrong.1.340 = 1340 just tell the prof.

Answer 39

but if they said its correct it doesnt matter.

Answer 40

well, if you have
\[ A= 2 \pi r^2 + 2\pi r \cdot \frac{1340}{\pi r^2} \]
can you simplify and then find the derivative with respect to r?

Answer 41

king answer it