Find the dimensions of the right circular cylinder of maximum volume that can be placed inside of a sphere of radius R.
Answers
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
Related Questions
A monthly budget with expenses is shown.
MONTHLY BUDGET
for a family of three
in San Antonio, Texas
Rent
$870
Food
$550
PR Child care
$375
Transportation
$480
Utilities
$400
Insurance
$235
Savings
$400
Taxes
$290
Monthly total
Which equation can be used to determine y, the minimum amount of money a family must earn to meet the requirements of this budget for one year?
y = 3600 x 12
y = 3600 + 7
y = 3600 x 4
y = 360052
Answers
Answer:
[tex]y = 3600 * 12[/tex]
Step-by-step explanation:
Given: Breakdown of Monthly Budget
Required
Determine the equation that shows minimum earnings in a year
First, we need to get the sum of the given list of budgets:
[tex]Budget = 870 + 550 + 375 + 480 + 400+235+400 + 290[/tex]
[tex]Budget = 3600[/tex]
The are 12months in a a year; So, the yearly budget (y) is:
[tex]Yearly\ Budget = Monthly\ Budget * Duration[/tex]
[tex]Yearly\ Budget = 3600* 12[/tex]
i.e.
[tex]y = 3600 * 12[/tex]
Estimate the area of the inregular shape. Explain your method and show your work.
Please help 100 points and brainliest
Answers
From the above coordinates: a = 7 length units, b = 4 length units and h = 5 length units. Therefore, approximate area = [(7+ 4)/2]*5 = 27.5 square units.
Hope it helps.
how would i slove for x??
Answers
Answer:
x=12
Step-by-step explanation:
First you need to find the 3rd angle.
180-118=x
x=62
Once you have that 3rd angle, set all the inside angles equal to 180
4x-6+5x+16+62=180 ---> set to 180
9x+72=180 -->combine like terms
9x=108 --> subtract 72 from both sides
x=12 -->divide both sides by 9
Ava bought 1.7 lb of plums and 7.2 lb of peaches how many was her total. Plums:$0.23. per pound peaches:$1.22 per pound
Answers
Answer:
0.391+8.42=8.811
8.811 in dollars is 10.42 United States Dollars
Step-by-step explanation:
Your answer is 10.42 c:
To demonstrate probabilities, a mathematics teacher had students draw cards from a bag which contained 26 red cards and
26 black cards. During class, the bag was dropped, and 5 red cards and 1 black card were lost.
Tell whether the loss of cards changes the probability of drawing a black card from the bag.
If so, was the probability increased or decreased? Support your answer by calculating the probability for each situation.
Answers
Answer:
decreased
Step-by-step explanation:
Use the inequality below to find the value of r .
150 - 5 r ≥ 87.5
a. r ≥ 12.5
b. r ≤ 12.5
c. r ≥ -(12.5)
d. r ≤ -(12.5)
Answers
How many shelves did Andrew stock per hour?
A. 15
B. 24
C. 30
D. 12
Answers
Answer:
D
Step-by-step explanation:
look at one hour and you will see that when it is at one hour it is a little bit over 10 but not enough to be 15
plz mark me brainliest like the other person didnt even explain.
F(x)=4x+5whsts the value of. F(-3). Is
Answers
Answer:
F(-3) = -7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
F(x) = 4x + 5
F(-3) is x = -3
Step 2: Evaluate
Substitute: F(-3) = 4(-3) + 5Multiply: F(-3) = -12 + 5Add: F(-3) = -7Combine like terms: 4 - 3m - 1 + 2m
Answers
Answer:
-m+3
Step-by-step explanation:
4 - 3m - 1 + 2m
4-1-m
-m+3
If a function f is increasing on (a,b) and decreasing (b,c), then what can be said about the local extremism of f on (a,c)?
Answers
Answer:
The point (b, f(b)) is a local maximum.
Can someone Please help with this problem,please help me ASAP !!!l
Answers
Answer:
I'd say B bcs it's the only thing that would fit with the shift on x axis and y axis
An 8-foot piece of twine costs $5.76. What is the price per inch?
Answers
Answer:
$0.06
Step-by-step explanation:
First, find how many inches are in 8 feet.
Since 1 foot is 12 inches, multiply 8 by 12:
8(12)
= 96
Then, to find the price per inch, divide the price by the number of inches:
5.76/96
= 0.06
So, the price per inch is $0.06
Answer:
$0.06
Step-by-step explanation:
There are 12 inches in a foot, and there are 8 feet all together, meaning there is 96 inches for $5.76.
Divided the cost y the number of inches to get the cost per inch,
5.76 divided by 96 = 0.06.
The density D of an object is the quotient of its mass m and its volume v
Answers
Please help and don’t answer with random letters I actually need the answer
Multiply x ^ (3/4) * x ^ (1/5)
1) x ^ (4/9)
2) x ^ (3/20)
3) x ^ (11/20)
4) x ^ (19/20)
Answers
Answer:
the answer is 4) i think
Step-by-step explanation:
i'm not sure but what i know, if the base is the same number, u can just add the power. for example, the bases is the same number which is x, so u can just solve the power which 3/4 + 1/5 then u get answer.
p/s: sorry for my english
Error Analysis A contractor purchases 4 dozen pairs of padded work gloves for $54.24. She
incorrectly calculates the unit price as $13.56 per pair for the expense report. What is the correct
unit price? What is the error?
The correct unit price is $
per pair.
Answers
Answer:
the unit rate for each pair is $1.13
Step-by-step explanation:
Okay this is how you would do this problem correctly:
we know that 4 dozen pairs of gloves cost $54.24 however we want to know what the cost is for one pair so we have to make a equation by dividing total cost by the number of glove pairs.
$54.24/4 dozen
the reason we are putting 4 dozen instead of just dividing $54.24 by 4 is because we want to know the unit price for each pair of gloves so it would actually look like this:
$54.24/4(12)
Dozen = 12
so we multiply 12 by 4 to get 48 pairs of gloves, we then divide $54.24 by 48 to find our unit rate of pricing for each pair:
$54.24/48 = 1.13
so now we place a dollar sign in front of 1.13 to get your answer:
for every pair bought it costs $1.13
So how did the Analysis A contractor get the wrong answer? well when she had bought the 4 dozen gloves she divided $54.24 by 4, which in this case would make it seem as though the gloves came in a 12 pack of gloves. However she was buying the gloves individually so she would have to multiply 4 by 12 before dividing the total number of gloves from $54.24.
A candy store sells caramels for $9/pound and chocolate for $12/pound. How much more is the cost of 2 pounds of caramel than 1.5 pounds of chocolate? *Show your work*
Answers
Answer:
The caramel is $0 more than the chocolate. In other words, they cost the same.
Step-by-step explanation:
Since we have 2 pounds of caramel and caramel costs $9/pound, the cost of 2 pounds of caramel can be found by this equation:
2lbs · $9 = $18
Since we have 1.5 pounds of chocolate and chocolate costs $12/pound, the cost of 1.5 pounds of chocolate can be found by this equation:
1.5lbs · $12 = $18
To find how much bigger the cost of caramel is than that of chocolate, we will subtract the total cost of the chocolate from the total cost of the caramel.
$18 - $18 = $0
Find the mean and the median of the data set. 31,32,36,31,30,35,33,30.
Answers
Answer:
Mean = 32.25
median = 31.5
Answer:
Median = 31.5
Mean = 32.25
Step-by-step explanation:
Number of data = 8
Ascending order:
30 , 30 , 31 , 31 , 32 , 33 , 35, 36
Median = Average of 4th and 5th term
= (31 + 32) / 2
= 63/2
= 31.5
Mean = Sum of all the observations /number of observations
= (31 + 32 + 36 +31 + 30 + 35 + 33 +30) / 8
= 258/8
= 32.25
Given: BC = DA, LCBD = ZADB
Prove: ABCD = ADAB
Statements
Reasons
I need help:(
Answers
A restaurant bill is $75. You want to leave about a 20% tip. Which is a 20% tip?
Answers
The tip is $15
(Conditionals)
TRUE OR FALSE:
If a number is a perfect square, then it has only 3 factors.
Answers
Answer:
False
I hope this helps!
Please help!
Part A: Which quantity is the independent variable?
Part B: Which quantity is the dependent variable?
Part C: Which graph is scaled appropriately for this situation?
Answers
Answer:
oooooooooooo
Step-by-step explanation:
mark me as a brainlist
answer fast!!!
A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 3100 seats. The students filled 32% of the seats in the theater. How many 6th graders went on the trip?
Answers
Answer:
992
Step-by-step explanation:
Answer:
38%
Step-by-step explanation:
1178 / 3100 = 0.38
38%
Albert's mom bought
5 2/3
pounds of potatoes. There are 5 people in Albert's
family and they all eat the same amount of potatoes.
How many pounds of potatos will Albert eat?
Answers
Hope this helps, correct me if I got it wrong :)
Solve for n: 0.22n = 6.6.
Answers
Answer:
30
Step-by-step explanation:
Solve for n: 0.22n = 6.6.
6.6/0.22 (because for example 3/3 and n/n= 1 so 0.22/0.22 = 1 so we have to divide 6.6 since it is part of the equation and we have to do it on both sides.)=30
Which of these figures shows parallel lines? Help please
Answers
Answer:
B a parrelel line means there not inerscting
Step-by-step explanation:
Write 2 equivalent ratios for 24/30
Answers
Answer:
Two equivalent ratios are: 4:5 and 48/60.
Step-by-step explanation:
Well, you can divide on the first one, and multiply on the second one. Hope it helps!
Type the following fractions in order from greatest to least:
5/4, 4/10, 5/12, ¼, 11/12
Write the decimals in the boxes from greatest to least:
0.5, 0.91, 0.04, 0.89, 0.51
Answers
Answer:
Just put the greatest number first and then the second greatest etc
HELP PLEASE!! NUMBER 6!!
You will get the brainiest if you can tell me how you did it, so I can finish doing them myself lol. If It comes back right, I will give it you instantly. Thank you very much.
Answers
Answer:
hey it's not clear....
Now that you’ve created your hypotheses, it’s time to prove them. First, look at the sum of two rational numbers. Let’s say they are two rational numbers, x and y. Because they’re rational, they can be written as a ratio of integers. Let x = and y = , where a, b, c, and d are integers and b and d do not equal 0. The process for finding the sum x + y in terms of a, b, c, and d is shown. Statement Reason substitution Create common denominators. Simplify. Based on this sum and using the closure property of integers, what conclusion can you make about the sum of two rational numbers? Explain your answer.
Answers
The question is missing parts. Here is the complete question.
Now that you've created your hypotheses, it's time to prove them. First look at the sum of two rational numbers. Let's say they are two rational numbers, x and y. Because they're rational, they can be written as a ratio of integers. Let [tex]x=\frac{a}{b}[/tex] and [tex]y=\frac{c}{d}[/tex], where a, b, c and d are integers and b and d do not equal 0. The process for finding the sum x + y in terms of a, b, c and d is shown in the figure below.
Based on the sum and using the closure property of integers, what conclusion can you make about the sum of two rational numbers? Explain your answer.
Answer: The sum of two rational numbers equals a rational number.
Step-by-step explanation: Rational number is defined as a number that can be made by dividing two integers.
Closure Property of Integers states the sum or subtraction of two integers always gives an integer.
Using the definition of rational and expanding the property, we can conclude that the sum of two rational numbers will result in a rational number, as demonstrated in the table below.
Answer This Question For Brainliest, Tip: It has to be right for brainliest
Answers
Answer:
B.
Step-by-step explanation:
Hope dis helps! :) I know for a fact its correct.
Answer:
The Correct answer for this question is B.
I hope this helps you answer this question.
:)