1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Morgarella [4.7K]
3 years ago
10

For the solid described below, find the dimensions giving the minimum surface area, given that the volume is 64 cm3. a closed cy

linder with radius r cm and height h cm.
Mathematics
1 answer:
stepladder [879]3 years ago
8 0
The volume of the cylinder is:
 V = pi * r ^ 2 * h = 64
 The surface area is:
 A = 2 * pi * r ^ 2 + 2 * pi * r * h
 We write the area as a function of r:
 A (r) = 2 * pi * r ^ 2 + 2 * pi * r * (64 / (pi * r ^ 2))
 Rewriting:
 A (r) = 2 * pi * r ^ 2 + 2 * (64 / r)
 A (r) = 2 * pi * r ^ 2 + 128 / r
 Deriving:
 A '(r) = 4 * pi * r - 128 / r ^ 2
 We equal zero and clear r:
 0 = 4 * pi * r - 128 / r ^ 2
 128 / r ^ 2 = 4 * pi * r
 r ^ 3 = 128 / (4 * pi)
 r = (128 / (4 * pi)) ^ (1/3)
 r = 2.17 cm
 The height is:
 h = 64 / (pi * r ^ 2)
 h = 64 / (pi * (2.17) ^ 2)
 h = 4.33 cm
 Answer:
 
The dimensions giving the minimum surface area are:
 
r = 2.17 cm
 
h = 4.33 cm
You might be interested in
Please answer the question. The picture is right below.
zhenek [66]
Hey man I’ve never seen nothing like this but I’d you’re doing math on ap classroom , man , GOOD LUCK
5 0
3 years ago
It took two people to complete carpeting in 10 days. How many more workers need to be hired to complete the same job in 4 days?
IRISSAK [1]

so two fellows did all the carpeting in 10 days.

now, how long did "1" fellow work only?  well, it worked for 10 days.

how long did the other fellow work for?  well, it was working alongside the first one, and it was there for also 10 days.

so the two guys working together, really did 10+10 = 20 "days worth of work".  So that the whole carpeting job can be done in 20 "days worth of work".

now if we want to finish it in 4 days, 20 ÷ 4 = 5.

so if we hire 5 guys, since each one will do 4 days worth, 5*4 = 20 <- the whole job.

4 0
3 years ago
Read 2 more answers
What is the volume of the prism<br>​
Alexus [3.1K]

Answer:

the answer is 18

Step-by-step explanation:

6 0
3 years ago
Joyce old 218 cupcakes of lemonade at his lemonade stand. What is 218 rounded to the nearest tens
MAXImum [283]

220

from 218 the 1 is in the tens column. this is the figure that needs to be rounded.

using the following rule

If the digit after the 1 is ≥ 5 then round 1 up to 2

If the digit after the 1 is < 5 then the 1 remains as 1

here the digit after the 1 is 8 so the 1 in the ten's column becomes 2 and the 8 is replaced by 0

218 ≈ 220 ( to the nearest ten )


7 0
3 years ago
What is an equation of the line in slope intercept form? M=2/3 and y intercept is (0,-3)
lana66690 [7]

Answer:

y= (2/3)x -3

Step-by-step explanation:

M is equal to the slope in y=mx+b form. And the y intercept is equal to (0, -3), therefore the b part of the formula is -3.

6 0
3 years ago
Other questions:
  • The length of a rectangle is five times the width. If the width is represented by z​, then build a variable expression that desc
    12·1 answer
  • the congruent sides of an isosceles triangle are each one unit longer than the length of the shortest side of the triangle the p
    11·2 answers
  • after geting 5 new rocks geogre gave half of his collection to susan.if george gave susan 36 rocks which equation could be used
    13·2 answers
  • ​Yesterday, Jack drove 33 and one half
    8·2 answers
  • Jan wants to lay sod on this lot. How
    8·1 answer
  • Which of the following are factors of 6x^2+30x-36
    7·1 answer
  • Help ASAP <br> What is the solution to this equation? (1/4)^x+1 =32
    10·1 answer
  • Need this to be done 5 minutes
    6·1 answer
  • Help please<br> What is the 33rd term of this arithmetic sequence?<br><br> 12, 7, 2, -3, -8
    11·1 answer
  • The question in line 9 is intended to
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!