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
lina2011 [118]
3 years ago
10

A solid is formed by adjoining two hemispheres to the ends of a circular cylinder. the radius of the hemispheres is the same as

the radius of the cylinder. the total volume of the solid is 16 cubic inches. what radius should the cylinder be to produce the minimum surface area?
Mathematics
1 answer:
nasty-shy [4]3 years ago
5 0
Total volume = Volume of Sphere + Volume of Cylinder
16 = (4/3)πr³ + πr²h
Express h in terms of r:
πr²h = 16 - (4/3)πr³
h = 16/πr² - (4/3)r

Next, let's solve for surface area:

Total Surface Area = SA of sphere + SA of cylinder
A = 4πr² + 2πrh
Substitute the expression for h:
A = 4πr² + 2πr[16/πr² - (4/3)r]
A = 4πr² + 32/r - (8/3)πr²

Find the derivative of A with respect to r and equate to zero.

dA/dr = 8πr - 32r⁻² - (16/3)πr = 0
Solve for r:
[(8/3)πr - 32/r² = 0]*r²
(8/3)πr³ - 32 = 0
r³ = 32*3/8π = 12/π
r = ∛(12/π)
<em>r = 1.56 inches</em>
You might be interested in
Select all the angle measurements that are correct
valina [46]

Answer:

a = 132

b = 132

d = 29

e = 29

f = 151

g = 24

h = 24

6 0
3 years ago
Define four symbolic constants that represent integer 25 in decimal, binary, octal, and hexadecimal formats
stealth61 [152]

Answer:

1) Decimal    25= (25)_{10}

2) Binary    25= (11001)_2

3) Octal   25= (31)_8

4) Hexadecimal   25= (19)_{16}

Step-by-step explanation:

Given : Integer is 25                      

To find : Represent integer in decimal, binary, octal, and hexadecimal formats.

Solution :

1) Integer into decimal - To convert into decimal the base goes to 10.

So, 25= (25)_{10}

2) Integer into binary - To convert into binary the base goes to 2, it form in 0 and 1 and we divide integer by 2.

Divide 25 by 2 and note down the remainders.

2 | 25

2 | 12    R=1    ←

2 | 6     R=0   ↑

2 | 3      R=0  ↑

2 | 1  →   R=1   ↑

So,   25= (11001)_2

3) Integer into octal - To convert into octal the base goes to 8 and we divide integer by 8.

Divide 25 by 8 and note down the remainders.

8 | 25

  | 3 →   R=1    

So,   25= (31)_8

4) Integer into hexadecimal - To convert into hexadecimal the base goes to 16 and we divide integer by 16.

Divide 25 by 16 and note down the remainders.

16 | 25

   | 1 →   R=9    

So,   25= (19)_{16}

3 0
3 years ago
Solve the formula V=3/4 LWH for W
aniked [119]
W= 3/4 divided by LH
5 0
3 years ago
Holly works in a stable. She's throwing straw into a stall that's 12 feet long by 8 feet wide. If she throws 12 cubic feet of st
Sloan [31]
Should take 8 minutes. I'm not totally sure; Pretty sure somebody else will get this right if I'm not.
5 0
3 years ago
Read 2 more answers
Let w = x2 + y2 + z2, x = uv, y = u cos(v), z = u sin(v). use the chain rule to find ∂w ∂u when (u, v) = (9, 0).
jasenka [17]
By the chain rule,

\dfrac{\partial w}{\partial u}=\dfrac{\partial w}{\partial x}\cdot\dfrac{\partial x}{\partial u}+\dfrac{\partial w}{\partial y}\cdot\dfrac{\partial y}{\partial u}+\dfrac{\partial w}{\partial z}\cdot\dfrac{\partial z}{\partial u}
\dfrac{\partial w}{\partial u}=2xv+2y\cos v+2z\sin v

We also have x(9,0)=0, y(9,0)=9, and z(9,0)=0, so at this point we get

\dfrac{\partial w}{\partial u}(9,0)=2\cdot9\cdot\cos0=18
7 0
3 years ago
Other questions:
  • 9(3n-9)-7-2n What is the answer to this I really need help.
    8·2 answers
  • -3(×+2)=12 what is x equal to
    8·1 answer
  • compare the decimal 6324. 50 as 6003 24.5 what comparison is correct 6, 3 24. 50 equals 6, 3 24.5 or 6003 24. 50 is greater than
    15·1 answer
  • Ashley has a can of vegetables that weighs 138 pounds. Each serving of vegetables is 14 of a pound. She wants to know how many f
    8·2 answers
  • You roll one die. What is the probability that you roll a 6?
    12·1 answer
  • Please someone please help, will mark you Brainliest
    15·2 answers
  • The upper-left coordinates on a rectangle are (-6,0)(−6,0)left parenthesis, minus, 6, comma, 0, right parenthesis, and the upper
    8·1 answer
  • Find the volume of the following. Round to nearest hundredths place:
    7·1 answer
  • (EASY MULTIPLE CHOICE I BEG YOU)
    6·1 answer
  • I need the answer to this I am very confused
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!