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]
2 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]2 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
The top of the table can be modeled with a cylinder, and the legs can be modeled with rectangular prisms.
Solnce55 [7]
The answer is B 3,703 in2

8 0
1 year ago
Read 2 more answers
0.8/y =2: 3/4 Please help
bulgar [2K]

Answer:

0.3

Step-by-step explanation:

0.8/y = 2 : 3/4

The value of y in the above expression can be obtained as follow:

0.8/y = 2 : 3/4

0.8/y = 2 ÷ 3/4

0.8/y = 2 × 4/3

0.8/y = 8/3

Cross multiply

0.8 × 3 = y × 8

2.4 = 8y

Divide both side by the coefficient of y i.e 8

y = 2.4/8

y = 0.3

Thus, the value of y is 0.3

8 0
2 years ago
Could you explain why the answer 125 was supposed to be negative while my answer 81 was correct?
hichkok12 [17]

Answer:

Step-by-step explanation:

Realize what (-5)^3 means

(-5)(-5)(-5)

25(-5)

-125

meanwhile

(-9)^2 is

(-9)(-9)

81

Basically a negative times a negative is always positive, but when a negative number is cubed (or raised to any odd exponent for that matter) the product will be negative.

5 0
2 years ago
Brian, Alex &amp; Colin share some money in the ratio 1:9:3.
fiasKO [112]

Answer:

Step-by-step explanation:

1:9:3

brian gets x

alex gets 9x

colin gets 3x

Brian and colin receive 40

x + 3x = 40

x = 10

alex gets 9x = £90

3 0
2 years ago
One baseball team played 36 games throughout their entire season. If this baseball team won 18 of those games, then what percent
gizmo_the_mogwai [7]
They have won 50% of their games.
7 0
2 years ago
Other questions:
  • Find the circumference of a circle with radius 1.4 in. long. Then use the approximation 3.14 for π and approximate the circumfer
    10·1 answer
  • HELP ME PLZZZ HURRY PLZ
    5·2 answers
  • Is B.) 8 the right answer to 2(4x - 6) = 6x - 4?
    11·1 answer
  • What is the value of X (x+40) (3x)
    14·1 answer
  • 82. Use properties of exponents to rewrite each expression with only positive, rational exponents. Then find the numerical value
    10·1 answer
  • What do I do????????
    14·1 answer
  • If in quadrilateral ABCD, AB = DC and BC = DA, then diagonals AC and BD Select one:
    15·1 answer
  • What do rectangles and parallelograms have in common?
    14·2 answers
  • Monica has 50 animals, 30 of the animals are cats. What percent of the animals are cats
    9·2 answers
  • Matt has started a car washing
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!