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
Nataliya [291]
2 years ago
11

Find the dimensions of the right circular cylinder of maximum volume that can be placed inside of a sphere of radius R.

Mathematics
1 answer:
Evgen [1.6K]2 years ago
3 0

This question is incomplete, the complete question is;

Find the dimensions of the right circular cylinder of maximum volume that can be placed inside of a sphere of radius R(10cm)

What is the maximum volume?

Answer:

a) Dimensions of the cylinder are; Radius = 8.1650 cm , Height = 11.547 cm

b) the maximum volume is 2418 cm³

Step-by-step explanation:

From the image

radius of the sphere is 10cm

radius of the cylinder is x and its height is 2y

so

The volume of cylinder  is V = πr²h = πx²(2y)

Get V as function of just one variable x² + y² = 100

x² = 100 - y²

Therefore V = π( 100-y² )(2y) = 200πy-2πy³

V will be a maximum when V' = 0

V' = 200π - 6πy² =0

y² = 200π / 6π = 100/3

y = √(100/3) = 5.7735

x² = 100 - y²

x² =100 - (100/3)

x = √(200/3)

x = 8.1650

So The maximum volume will occur when the radius is 8.1650 cm

and the height 2y is 2(5.7735) = 11.547 cm

The maximum volume is

πr²h = π(8.1650)² (11.547 )  

= 2418 cm³

Therefore the maximum volume is 2418 cm³

You might be interested in
Solve the system by graphing.<br> y = x+2<br> 2x-y=-1
N76 [4]

Answer:

The intersection is at (1,3) and the answer is in the graph. (see image below)

Step-by-step explanation:

5 0
1 year ago
12 less than Goran's age is 44.<br> Use the variable g to represent Goran's age
lions [1.4K]

Answer:

12-g=44

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Help me I'm struck it to hard I dont get it ​
lbvjy [14]
You add four four times !
5 0
3 years ago
A student pays for 8.9 pounds of apples with a $10 bill. How much change does the student receive if the apples are .99 per poun
nexus9112 [7]
The student will receive $1.2 

8.9 x .99 =  8.8
10 - 8.8 = 1.2
3 0
3 years ago
Read 2 more answers
What is the sum of the solutions of 2|x−1|−4= −2 2x-1-4= -2
Maru [420]
<span>The problem is as following :
</span>
<span>What is the solutions of 2|x−1|−4= −2
</span>
===============================================
<span />
Solution:

<span>The equation is  ⇒⇒  2|x−1|−4= −2  →   add 4 to both sides
</span>
<span>∴ 2|x−1| -4 + 4= −2+4
</span>
<span>∴  2|x−1|= 2  → divide over 2
</span>
<span>∴ |x−1|= 1
</span><span>
</span><span>According to absolute rules:
</span>
<span>∴ x-1 = 1  or   x-1 = -1
</span>
<span> ∴ x = 2     or    x = 0  
</span>
<span>∴ x = {0,2}
</span>

So, the solution of the equation is {0,2}
7 0
3 years ago
Other questions:
  • 2/3 of all the people who attended a certain party arrived by 8:00 PM. How many people arrived by 8:00 PM?
    14·1 answer
  • In ABC AD and BE intersect each other at point q according to a theorem on medians q divides AD in the ratio 2:1 what are the co
    14·1 answer
  • Lim [abs(x-7)] / [x-7]<br> x -&gt; 7 (-)
    7·1 answer
  • Please solve and I will give brainliest!
    11·2 answers
  • Please help me! this is timed!
    7·1 answer
  • A fruit punch mixture is made of Orange juice, Pineapple juice, and Cranberry juice in a 3:5:7 ratio. How much of each juice typ
    6·2 answers
  • Sahil has a fish tank in the shape of a cuboid, as shown in the diagram
    15·1 answer
  • ‼️‼️Find the volume of the cylinder.‼️‼️
    8·1 answer
  • Yesterday Jefferson slept for 7 hours and 45 minutes. Katherine slept for 8 hours and 25 minutes. How much longer did Katherine
    9·1 answer
  • Which is correct about how air typically moves? (1 point) O Air moves from high-pressure areas to low-pressure areas. O High-pre
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!