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
Temka [501]
3 years ago
8

Surface Area of a can is 517.8 cm^2. Maximize the volume of this can using the measured surface area.

Advanced Placement (AP)
1 answer:
mafiozo [28]3 years ago
7 0

Answer:

r = 5.24 --- Radius

h = 10.48 --- Height

Explanation:

Given

Object: Can (Cylinder)

Surface\ Area = 517.8cm^2

Required

Maximize the volume

The surface area is:

S.A = 2\pi r^2 + 2\pi rh

Substitute 517.8 for S.A

517.8 = 2\pi r^2 + 2\pi rh

Divide through by 2

258.9 = \pi r^2 + \pi rh

Factorize:

258.9 = \pi r(r + h)

Divide through by \pi r

\frac{258.9}{\pi r} = r + h

Make h the subject

h = \frac{258.9}{\pi r} - r --- (1)

Volume (V) is calculated as:

V = \pi r^2h

Substitute (1) for h

V = \pi r^2(\frac{258.9}{\pi r} - r)

Open Bracket

V = 258.9r - \pi r^3

Differentiate V

V' = 258.9 - 3\pi r^2

Set V' to 0

0 = 258.9 - 3\pi r^2

Collect Like Terms

3\pi r^2 = 258.9

Divide through by 3

\pi r^2 = 86.3

Divide through by \pi

r^2 = \frac{86.3}{\pi}

r^2 = \frac{86.3*7}{22}

r^2 = \frac{604.1}{22}

Take square root of both sides

r = \sqrt{\frac{604.1}{22}

r = 5.24

Recall that:

h = \frac{258.9}{\pi r} - r

Substitute 5.24 for r

h = \frac{258.9}{\pi * 5.24} - 5.24

h = \frac{258.9*7}{22 * 5.24} - 5.24

h = \frac{1812.3}{115.28} - 5.24

h = 15.72 - 5.24

h = 10.48

Hence, the dimension that maximize the volume is:

r = 5.24 --- Radius

h = 10.48 --- Height

You might be interested in
I have 3 cute pet rats 1 rat thats a 1y old and 2 baby around 6-8 month there still soooo cute any questions
romanna [79]

Answer:

what color are they

Explanation:

7 0
3 years ago
Read 2 more answers
This map shows the shifting center of american population in the first two centuries of it's existence. What might BEST account
iren2701 [21]
What’s the map? And is this for human geo?
6 0
2 years ago
Point D is located on MV .The coordinates of D are (0,−3/4).What fraction of the distance from M to V is MD?
dedylja [7]
Where is the rest of the question
6 0
1 year ago
Why do the courts play so large a role in deciding what our civil liberties should be?
kondor19780726 [428]

The court are independent of the executive and legislative branches, both of which will respond to public pressures. In wartime or in their crisis periods, people want " something done."

hope this helps:)sorry if it doesnt

8 0
3 years ago
Can someone please explain the Chechen conflict with Russia in 1999?
PtichkaEL [24]
Https://youtu.be/wX-xs9VJ-BI
https://youtu.be/ap0BiR3NF6w


These helped me. I hope they help you.
6 0
3 years ago
Other questions:
  • Please help me with some examples of the 4 bullets I’m really behind I’ll give brainliest
    14·1 answer
  • Study the following quote. Then answer the question that follows.
    9·2 answers
  • Which of these is a characteristic of intraregional migration? A) It is seasonal B) It is sporadic. C) It is permanent. D) It is
    5·2 answers
  • The upscale Ethan Grant Company has created a new cologne called Ethan for men and a "matching" perfume called Ethan Femme. The
    7·1 answer
  • Write one to two paragraphs describing the relationship between the management of natural resources, the
    15·1 answer
  • Most of the __________ gas in the atmosphere results from the activity of producer organisms.
    15·2 answers
  • Which expensive irrigation method uses tubes that release water slowly to decrease the amount of water lost to
    9·1 answer
  • How many times a year is the Earth at its average distance from the Sun
    5·1 answer
  • Which region has the highest elevation?
    5·2 answers
  • What are three factors that affect the violence of a volcanic eruption?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!