explain how the formula for the volume of a cone is derived

Answers

Answer 1

Answer:

The volume of a cone is 1 3 π r 2 h \frac { 1 } { 3 } \pi r ^{ 2 } h 31πr2h, where r denotes the radius of the base of the cone, and h denotes the height of the cone.

Step-by-step explanation:

(happy to help)

Answer 2

Final answer:

The volume of a cone is derived using the principle of integrating infinitesimally thin discs along the height of the cone, given by the formula V = ⅓πr²h.

Explanation:

The formula for the volume of a cone is derived using calculus and geometric principles. Consider a cone generated by rotating a line around one of the coordinate axes. If we know the formula for the area A of a circle, it can be extended to find the volume of a cone. The area A of a circle is πr², where r is its radius. The formula for the volume V of a cone is ⅓ × base area × height, which can be expressed as V = ⅓πr²h, with h being the cone's height.

Using integral calculus, the cone's volume is found by stacking infinitesimally thin discs (each with volume πr²dx, where dx is the disc's thickness) along the cone's height. The radius r changes linearly from the base to the apex, following the relationship r = (h - x)tan(a), where a is the semivertical angle of the cone. Thus, you integrate from the apex (0) to the base (h) to find the entire volume of the cone.


Related Questions

I need help with question 2. Anything is appreciated:)

Answers

1x + 8 = 10 + 0.5x

1x - 0.5x = .5x

.5x + 8 = 10

10 - 8 = 2

2/.5 = 4

Therefore, it will take 4 years for the two trees to have grown to the same height.

Answer:

8 years

Step-by-step explanation:

Match the following items.
Plane
Point
Line
Ray
Line segment

Answers

Answer:

The first one is a line because a line extends infinitely in both directions which the arrows indicate.

The second one is a plane since it is a 2-dimensional shape.

The last one depicts 2 rays because rays have one endpoint, but extend infinitely in the other direction.

Answer:

The first one is a line because a line extends forever in both directions which the arrows indicate.  

The second one is a plane since it is a 2-dimensional shape.  

The last one depicts 2 rays because rays have one endpoint, but extend infinitely in the other direction.

Step-by-step explanation:

I am not copying the other person and I think that he should be marked Brainliest

This graph shows a proportional relationship between the amount of money in Kaitlyn's savings account and the number of days Kaitlyn has been saving money.
Kaitlyn's Savings
Account
Amount in
Savings ($)
2 3 4 5
Number of Days
Which statement identifies the correct slope, and the correct interpretation of the slope for this situation?
The slope of the line is so, so Kaitlyn's savings rate is $1 dollar every 60 days.
®
The slope of the line is
so Kaitlyn's savings rate is $60 dollars every day.
©
The slope of the line is
so Kaitlyn's savings rate is $60 dollars every day.
The slope of the line is so, so Kaitlyn's savings rate is $1 dollar every 60 days.

Answers

Answer:

c

Step-by-step explanation:

what is the rate of change between
(0.5,-3.7) and (0.7 -3.4)?​

Answers

For (.5,-3,7) the ratio of change is 4.2 and for (0.7-3.4) is 4.1 the change between both however is a single decimal or .1

Can someone answer this question please answer it correctly if it’s corect I will mark you brainliest

Answers

Let's put all of these into percent form.

P(Guilty) = 0.25 = 25%

P(Innocent) = 55%

P(Retrial) = 1/5 = 0.2 = 20%

Next, we need to order them from least to most likely. The least likely event to occur would be the smallest percent, then the next smallest, etc.

Order: Retrial, Guilty, Innocent

Hope this helps! :)

Answer:

retrial, guilty, innocent

Step-by-step explanation:

We need to first convert these into the same kind of format, whether it's all decimals, all fractions, or all percentages. Let's just do decimals.

The guilty is already a decimal: 0.25.

The innocent is a percent. Remember that % simply means "out of 100", so 55% is 55/100. When we divide by 100, we move the decimal point two places to the left, so 55/100 = 0.55.

The retrial is a fraction. Just try to remember that 1/5 always equals 0.2.

The least likely event will be the smallest decimal, which is 0.2. The most likely event is the largest decimal, which is 0.55. So, the order is:

retrial, guilty, innocent

What is the value of x:
5x + 4 = 2x +22

How would you solve this question?

Answers

Answer:

6

Step-by-step explanation:

1. Combine like terms (x)

Subtract 2 from one side to move it to the other side. *What you do to one side, you must do to the other.

You now have: 5x(-2x)+ 4= 22

Subtract 2 from 5= 3x

You now have 3x+ 4 = 22

*You can’t add 4 to 3x because they are different terms (can’t add whole numbers with an x value)

Subtract 4 to move it to the other side;

3x= 22-4

22-4 = 18

3x=18

Divide by 3 to remove 3 from one side

X= 6 (because 18/3= 6

Answer: x = 6

Explanation: This problem can be done either of two ways by putting the variables together on the left and the numbers together on the right or vice versa.

If we put our variables together on the left and our numbers together on the right, we would start by subtracting

2x from both sides to get 3x + 4 = 22.

Next, we subtract 4 from both sides to get 3x = 18.

Finally, we divide both sides by 3 to get x = 6.

Note that we can check our answer by plugging 6 back in

for both of the x's in the original equation.

So go ahead and check the answer and see if it works.

charlee wants to send postcards to all of her family and friends but she does not have any postcards she does have 3 large sheets of poster board,each sheet can be cut into 12 postcards how many postcards can charlee make

Answers

Answer:

36

Step-by-step explanation:

You do 12*3 because if 1 sheet of poster board can make 12 post cards, and you have 3 poster boards you will need 3 lots of 12 which is equivalent to 3*12!

Hope this helps!

GIVING BRANLIEST!!!
Which ordered pair is the solution to this system of equations?

x = 6

y - 3x = -8


Group of answer choices

(6, 10)


(10, 6)


(6, -26)


(-26, 6)

Answers

Answer:

I believe it's (6,10).

evaluate the expression for p=2
81-p

Answers

Answer:

79

Step-by-step explanation:

81 - p

Let p =2

81-2

79

Y= x+8
2x+y=-10

A. (2,6)
B. ( 2,-6)
C. ( -6,2)
D. (6,2)

Answers

The answer is B
Glad I could help:)

29.25 is what percent of 78

Answers

Answer:

2

Step-by-step explanation:

Answer:

thirty - eight percentage

Step-by-step explanation:

You are going to have to divide for this question.

29.25 / 78 = 0.375

0.375 ≈ 0.38

0.38 * 100 = 38

So 29.25 is 38% of 78.

Please help!!! How do I turn these problems into inequalities?!?!

Answers

4500 ≤ 1400 + .05x, where x = sales

800 + .15s = 5000, where s = sales <-- this isn't an inequality, because it's asking for the exact amount of sales Ling needs to get.

(85+76+94+81+y)/5 ≥ 85, where y = next test score

Answer:

5. at least $62,000 worth of cars

6. $28,000 on sales

7. at least an 89

Step-by-step explanation:

5. We have a base salary of $1400 and the earning is 5% on sales (in other words, of the total profits from sales, the salesperson gets 5% of that). If s represents sales, we can say that the salesperson earns:

1400 + 0.05 * s

We want the end product to be at least $4500, so:

1400 + 0.05s ≥ 4500

0.05s ≥ 3100

s ≥ $62,000

The salesperson needs to sell at least $62,000 worth of cars.

6. This is similar to the previous question. Say the number of sales is s. Then, we have:

800 + 15% * s = 5000

800 + 0.15s = 5000

0.15s = 4200

s = 28,000

Ling needs to sell $28,000 on sales.

7. Let's say the last score is x. The average is found by adding all the test scores and dividing by the number of tests:

(85 + 76 + 94 + 81 + x) / 5 ≥ 85

336 + x ≥ 425

x ≥ 89

Latrell needs to earn at least an 89 on his next test to keep his average at 85 or higher.

QUESTION 27 • 5 POINTS
Marco needs to mix a solution that is 8% iodine with one that is 44% iodine to obtain 200 liters of a solution that is 29%
iodine. Using a system of linear equations, find how many liters of the 8% iodine solution will be required to create the new
solution. Round to the nearest liter.

Answers

Answer:

83 liters

Step-by-step explanation:

If we call the amount of liters of the 8% iodine solution by x and the amount of liters of the 44% iodine solution by y, we can write the following equations:

x + y = 200

x*0.08 + y*0.44 = 200*0.29

From the first equation, we have that y = 200 - x

Using this value of y in the second equation, we have that:

0.08x + (200 - x)*0.44 = 58

0.08x + 88 - 0.44x = 58

0.36x = 30

x = 30/0.36 = 83.3333 liters

Rounding to nearest liter, we have x = 83 liters

You deposit $275 each month into this account (7% APR
compounded monthly), how much money will be in the account
after 18 years (216 months)?

Answers

Answer:

120,050.58

Step-by-step explanation:

CIRCUMFERENE QUESTION. If you get it correct, immediant brainlist! 5 stars and thanks for ALL answers! If both people get it right, whoever answers first gets the brainlist. If both get incorrect, only 5 stars and thanks. If the question already has had 2 people answering, please try to answer in the "ask for details" section! I will give thanks.

Answers

Answer:

The circumference is about 44 in.

Step-by-step explanation:

Assuming that 7 in is the radius of the pizza:

[tex]C=2\pi r[/tex]

[tex]C=2\pi 7\\C=14 \pi\\C=43.98 \text{in}[/tex]

How does the shape of a cross-section of a 3D figure parallel to the base relate to the volume of the 3D figure?

Answers

Answer:

The shape of each cross-section of a 3D figure,  relates to the volume because the area of the cross-section is determined by its shape and the area of this cross section is in the sum that calculates the volume of this 3D figure.

Step-by-step explanation:

An infinite sum of all the all the cross-sections of a 3D figure parallel to the base equals the volume of that 3D figure.

If r = 10 units and x = 14 units, then what is the volume of a cylinder?

A.

140 cubic units

B.

1,400 cubic units

C.

480 cubic units

D.

5,600 cubic units


I have no idea so please teach me.

Answers

it would be (B) it’s kinda obvi because it can’t be a or c and d is to much

Solve the riddle.

Two-thirds of a number increased by five is the same as negative two-sixths of a number increased by fourteen.

Two-thirds x + 5 = negative StartFraction 2 Over 6 EndFraction x + 14

What is the number?

Answers

Answer:

The correct answer is 9.

Step-by-step explanation:

Hope this helps you out!

~Lexi

Answer: 9

Step-by-step explanation:

got it right me

Need ASAP worth 100 points

Answers

That's the Riemann Zeta function. Here s is a complex number.  If you can prove that all the non-trivial zeros of ζ(s) (which includes its analytic continuation to the entire complex plane) are on the line Re(s) = -1/2 then you will become a famous mathematician.  You didn't even ask a question; not a very auspicious start, but don't give up.

If we restrict s to the reals, as Euler first did, we can prove there are an infinity of primes.  Ever since the Zeta function has been closely related to the prime numbers.

One fun fact is ζ(-1) = -1/12, which has spawned lots of bad math claiming the sum of the natural numbers is -1/12,

[tex]-\dfrac{1}{12} = \zeta(-1) = \dfrac{1}{1^{-1}} + \dfrac{1}{2^{-1}} + \dfrac{1}{3^{-1}} + ... = 1 + 2 + 3 + 4 + ...[/tex]

Here it is in Ramanujan's first letter to Hardy.

Answer:

Hes right

Step-by-step explanation:

Complete the table for the given rule.
Rule: y= 1/3x

Answers

Answer:

12 - 4

3 - 1

18 - 6

Step-by-step explanation:

This is simply a matter of pluggin in the method, so let's do it shall we?

It wants you to put the a third of each number, so you'll divide each number by three to get what the third is!

VISUAL REPRESENTATION:

12÷3 = 4

3÷3 = 1

18÷3 = 6

The completed table for the given rule y = (1/3)x is given.

To complete the table for the given rule y = (1/3)x, we need to substitute the values of x into the equation and calculate the corresponding values of y.

Using the given rule y = (1/3)x:

1. For x = 12:

y = (1/3) * 12 = 12/3 = 4.

2. For x = 3:

y = (1/3) * 3 = 3/3 = 1.

3. For x = 18:

y = (1/3) * 18 = 18/3 = 6.

Now, the completed table for the given rule is:

x   | y

--------

12  | 4

3   |  1

18  | 6

To know more about rule, refer here:

https://brainly.com/question/15155685

#SPJ2

Students in the 7th and 9th grades were surveyed about whether they participate in a school sport. Some of the survey results are listed here.

50 of the 250 students surveyed participate in a school sport.
Of the 90 students in 7th grade, 72 of them do not participate in a school sport.
32 of the 9th-grade students participate in a school sport.
128 of the 9th-grade students do not participate in a school sport.

This information is shown in the two-way frequency table below. Drag numbers into the empty spaces to complete the table.

Answers

Answer:

18-72=90

32-128=160

50-200=250

Answer: 18, 160, 200

Step-by-step explanation: hope it helps...!

Help I’ll do anything just help

Answers

Answer:

[tex]1) {n}^{2} - 81 \\ (n - 9)(n + 9)[/tex]

[tex] 2) \: \: {a}^{2} - 121 \\ (a - 11)(a + 11)[/tex]

[tex]3) \: \: {n}^{2} - 16 \\ (n - 4)(n + 4)[/tex]

[tex]4) \: \: 9 {x}^{2} - 144 \\ {3}^{2} {x}^{2} - {12}^{2} \\ (3x - 12)(3x + 12)[/tex]

[tex]5) \: 2 {x}^{2} - 9 \\ (2x - 3)(x + 3)[/tex]

[tex]6) \: \: 4 {w}^{2} - 9 \\ {2}^{2} {w}^{2} - {3}^{2} \\ (2w + 3)(2w - 3)[/tex]

[tex]7) \: \: 4 {n}^{2} - 1 \\ {2}^{2} {n}^{2} - {1}^{2} \\ (2n + 1)(2n - 1)[/tex]

[tex]8) \: \: 1 - 16 {x}^{2} \\ {1}^{2} - {4}^{2} {x}^{2} \\ (1 - 4x)(1 + 4x)[/tex]

[tex] 9) \: \: {x}^{2} - {y}^{2} \\ (x - y)(x + y)[/tex]

[tex]10) \: \: 9 - {c}^{2} \\ {3}^{2} - {c}^{2} \\ (3 - c)(3 + c)[/tex]

[tex]11) \: \: {n}^{2} - 25 \\ {n}^{2} - {5}^{2} \\ (n + 5)(n - 5)[/tex]

[tex]13)49 - 4 {a}^{2} \\ {7}^{2} - {2}^{2} {a}^{2} \\ (7 - 2a)(7 + 2a)[/tex]

[tex]14) {a}^{2} {b}^{2} - {c}^{4} \\ (ab - {c}^{2} )(ab + {c}^{2} )[/tex]

[tex]15) \: \: 4 {x}^{2} {y}^{2} - 9 {z}^{2} \\ {2}^{2} {x}^{2} {y}^{2} - {3}^{2} {z}^{2} \\ (2xy - 3z)(2xy + 3z)[/tex]

hope this helps

sorry, I don't know how solve the 12th one.

thanks.

What interval includes all possible values of x, where -306 - 2x) > 4x + 12?

Answers

Corrected Question

What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12?

A. (–∞, –3]   (B) [–3, ∞)  (C)(–∞, 15]  (D)[15, ∞)

Answer:

(D)[15, ∞)

Step-by-step explanation:

We want to determine what interval of x includes all possible values of x in: [tex]-3(6 - 2x) \geq 4x + 12[/tex]

First, we open the bracket on the Left hand side

[tex]-18+6x \geq 4x + 12[/tex]

Next, we collect terms with x on the Left hand side and constants on the right hand side.

[tex]6x-4x \geq 12+18\\2x\geq 30\\$Divide both sides by 2\\x \geq 15[/tex]

Therefore, the interval of x which includes all possible values of x is [15, ∞).

Option D is the correct option.

4 If y = 2x + 1, what is X=-3?
A 5
B - 7
C -5
D 6

Answers

Answer:

c

Step-by-step explanation:

y=2(-3)+1

y=-6+1

y=-5

USE SUBSTITUTION

Answer:

c) -5

Step-by-step explanation:

plug in the x.

y= 2(-3)+1

y= (-6)+1

y= -5

Which number produces an irrational number when added to 1/3?

Answers

Answer:

B

Step-by-step explanation:

Since all other numbers are rational numbers, and with pi being irrational, adding 1/3 to 2pi would keep it irrational.

Answer:

2 pi

Step-by-step explanation:

So lets try and check , why to be lazy ?

1/3+2/3 =1 , as we all know 1 is a rational number.

.

so lets move to another option

Now ,

1/3+2 pi = 7/2 pi , its an irrational number .

we already got the answer , but we will try others too .

( Because i have so much amount of time , let me kill some of it! )

1/3+2 = 2.3333333.... which is again a ratiomal number .

1/3+0.166 = 0.49933333333... which is again a rational number .

Additional Information

An irrational number is a number that is nor terminating , nor recurring .The set of rational and irrational number is called real numbers .No rational number is irrational number , and no irrational number is rational number .

The histogram shows the distributions of essay scores for high school sophomores and juniors in a contest. Which comparison of the distributions is true? Both distributions are nearly symmetric. Both distributions are right-skewed. The distribution of sophomores’ scores is right-skewed, and the distribution of juniors’ scores is left-skewed. The distribution of sophomores’ scores is left-skewed, and the distribution of juniors’ scores is right-skewed.

Answers

Both distributions are nearly symmetric. And the correct answer is A.

What is a distribution?

The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.

A histogram is a graphical illustration of information in bars of diverse heights.

A histogram displays the shape and spread of continuous sample data.

The true statements about the data of essay scores for high school sophomores and juniors in a contest are;

the juniors tended to have higher essay scores than the sophomores, the medians of both data sets are equal,

and the histogram is the best way to show that both distributions are nearly symmetric.

Therefore, distributions are symmetric.

To learn more about the distributions;

https://brainly.com/question/29062095

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What is the area of the square?
A square has side lengths of 10.6 yards.
21.2 yd2
36 yd2
42.4 yd2
112.36 yd2

Answers

D is your answer:)

112.36 yd^2

Help please! I need an explanation.

Answers

Answer:

A

Step-by-step explanation:

Answer:

6.5

Step-by-step explanation:

I substituted y into the equation

so I set it up like 3x-5(-5x+32)=22

and solved from there

Garrett was given two numbers, 1.6 and 25, and was instructed by his teacher Mrs. Hellie to find
the sum. Garrett found the sum and stated that the answer was a rational number. Do you agree or
disagree with Garrett? Justify your answer.

Answers

Answer:

I agree with Garret.

Step-by-step explanation:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

To get rid of the decimal point in the numerator, we count the numbers after the decimal in 26.6, and multiply the numerator and denominator by 10 if it is 1 number. Therefore, in this case we multiply the numerator and denominator by 10 to get the following fraction:

266 / 10

Then, we need to divide the numerator and denominator by the greatest common divisor(GCD) to simplify the fraction.The GCD of 266 and 10 is 2. When we divide the numerator and denominator by 2, we get the following:

133 / 5, which is ni a p/q form.

The distance between City A and City B is 250 miles. A length of 1.7 feet represents this distance on a certain wall map. City C and City D are 3.74 feet apart on this map. What is the actual distance between City C and City​ D?

Answers

Step-by-step explanation:

You have to apply a proportion:

250 : 1.7 = x : 3.74

250 × 3.74 = 1.7 × X

X = 250×3.74 / 1.7 = 550

Answer:

549.78 miles

Step-by-step explanation:

250m / 1.7ft = ~147 miles/ft

147 * 3.74 = 549.78

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