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
Estimate. then ,divide using the standard algorithm and check<br> 45.15/21
insens350 [35]
I estimated to 45 then divided 21 and got about 2.1


7 0
3 years ago
One option in a roulette game is to bet $ 6
Eduardwww [97]

Answer:

<h2>We have 47% of chances to win those six bucks.</h2>

Step-by-step explanation:

In this problem we need to find the probabilty of winning thos $6.

According to the problem, we win $6 if we hit one red. We know that there are 18 red compartments, 18 black compartments and 2 neither red nor blakc, for a total of 38 compartments.

We need to use the standard probabilty definition which is the ratio between the number of events and the total number of outcomes. So,

P=\frac{18}{38} \approx 0.47

Which is equivalent to 47% of chances.

Therefore, we have 47% of chances to win those six bucks. (The Casino has the odds in their favor)

5 0
2 years ago
Help ASAP!!
nexus9112 [7]
The answer is 66 units
6 0
3 years ago
Read 2 more answers
Which one is it A B C D
vovangra [49]

Answer:B

Step-by-step explanation: Alternate exterior angles theorem

3 0
3 years ago
Which expression is equivalent to (x Superscript 27 Baseline y) Superscript one-third?.
marin [14]

To solve the problem we must know the basic exponential properties.

<h3>What are the basic exponent properties?</h3>

{a^m} \cdot {a^n} = a^{(m+n)}

\dfrac{a^m}{a^n} = a^{(m-n)}

\sqrt[m]{a^n} = a^{\frac{n}{m}}

(a^m)^n = a^{m\times n}

(m\times n)^a = m^a\times n^a

The expression can be written as x^9\sqrt[3]{y}.

Given to us

  • (x^{27}y)^\frac{1}{3}

(x^{27}y)^\frac{1}{3}

Using the exponential property(m\times n)^a = m^a\times n^a,

=(x^{27}y)^\frac{1}{3}\\\\=x^{\frac{27}{3}}\times y^\frac{1}{3}\\\\=x^9\times y^\frac{1}{3}

Using the exponential property \sqrt[m]{a^n} = a^{\frac{n}{m}},

=x^9\times y^\frac{1}{3}\\\\=x^9\times \sqrt[3]{y}\\\\=x^9 \sqrt[3]{y}

Hence, the expression can be written as x^9\sqrt[3]{y}.

Learn more about Exponent properties:

brainly.com/question/1807508

5 0
2 years ago
Read 2 more answers
Other questions:
  • a diver is atan elevation of -18 feet relative to sea level. the diver desceends to an undersea cave that is 4 times as far from
    5·1 answer
  • What's -26.3 plus -12.6
    5·2 answers
  • JLYK , I also need the math
    6·1 answer
  • Simplify m+{n-[p+q-(m-n+p-q)]}​
    13·1 answer
  • Great amounts of electromagnetic energy from our sun travels through space. Which is the best answer about electromagnetic waves
    13·1 answer
  • A faucet is used to add water to a large bottle that already contained some water. After it has been filling for 55 ​seconds, th
    9·1 answer
  • Are rectangles ABCD and WXYZ congruent? Why or why not? Yes, all right angles were preserved. Yes, both rectangles have an area
    14·2 answers
  • Help fast plez 10 points
    8·1 answer
  • In a study of texting speed, 45 adults aged 18-22 were randomly chosen. Each person was asked to the following phrase exactly "H
    7·1 answer
  • Solve the equation 5(x + 2) = 6x + 3x − 14, and show your work. (5 points)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!