How are formulas for the volume of a cylinder, pyramid, and cone derived?

Answers

Answer 1

Answer:

Calculus-based analytic geometry makes the cylinder, pyramid, and cone from "solids of revolution". From there, they can measure the length or radius of the base, and then the height. This is true even if the solid of revolution is along the X axis intead of the Y axis. Then someone "figured out" the formula, just like they did with a cube, and proved it.


Related Questions

Write a short para based on how the pandemic has affected travelling.

Answers

Answer:

Unlike many of history’s great tragedies, the coronavirus pandemic never stunned us with one catastrophic event. Instead, the deadly problem quietly snaked its way around the world, devastating millions as it grew into a global health crisis since it first surfaced in November.

Our realities shifted slowly at first, and before we knew it, the coronavirus took over completely.

As we closed borders, canceled events and self-quarantined at home on a mass scale, the travel industry, as well as most other sectors, began to nosedive. The collective effort to save lives meant economic catastrophe for an industry that profits from people leaving their houses.

The wound inflicted by the pandemic on the travel industry is deep, and it hasn’t stopped bleeding yet.

In a May 20 call with analysts, Royal Caribbean Cruises chief executive Richard Fain recalled how drastically travel changed after the 9/11 terrorist attacks — and how the “new normal” eventually just became normal. He expects to see a similar phenomenon in the post-coronavirus world.

sorry it didnt let me send it so i took a lictire of it stay safe out there in the world wherever you are to let you know god is with you all the time if your in fear pray to him and he will take the fear away from you. anyways, stay safe and love you all!❤

The sides of an oblong are in the ratio of 4:3. The oblong has a length of 12 cm and is increased by a scale factor of 2.5. What will the increased width be

Answers

Answer:

If the scale factor is increased in 2.5, the increased width will be:

22.5 cm

Step-by-step explanation:

Remember that an oblong is longer than it is wide, by this reason, the ratio of 4:3 could mean, if we give a number, by each 4 cm in the length, there is 3 cm in the width, in this form, if the oblong has a length of 12 cm, the width is:

4 cm ⇒ 3 cm12 cm ⇒ x

So:

[tex]x=\frac{12 *3}{4}[/tex][tex]x=\frac{36}{4}[/tex][tex]x=9[/tex]

Then, the original width is 9 cm, as the scale factor must be increased 2.5, we can multiply the found width to obtain the increased width:

Increased width = 9 cm * 2.5Increased width = 22.5 cm

As you can see, the increased widt will be 22.5 cm.

What is the factorization? x2 + x – 12

Answers

Answer:

(x+4)(x-3)

Step-by-step explanation:

The value of the square root of 25+144 is 13. True or false

Answers

It is true. The Square root of 169 (25 + 144) is 13. 13×13 is 169

Answer:

true i tested it out myself.

Step-by-step explanation:

(PLEASE HELP) 17. Jon read 3/8 of a book the
first day. 1/3 the second day.
and 1/4 the third day. On the
fourth day he finished the book.
What part of the book did Jon
read on the fourth day?

Answers

Answer:

[tex]\frac{1}{24}[/tex]

Step-by-step explanation:

24 is a common multiple so ill just use that as a denominator:

3/8 = 9/24

1/3 = 8/24

1/4 = 6/24

so then adding those up:

[tex]\frac{9}{24}[/tex] + [tex]\frac{8}{24}[/tex] + [tex]\frac{6}{24}[/tex] = [tex]\frac{23}{24}[/tex]

then whats left is 1/24 left to read, which cant be simplified so [tex]\frac{1}{24}[/tex]

Answer:

   [tex]\frac{1}{24}[/tex]

Step-by-step explanation:

Let x be the part of the book he read on fourth day.

[tex]\frac{3}{8} + \frac{1}{3} + \frac{1}{4} + x = 1[/tex]

[tex]LCM \ of \ 8, 3 , 4 = 24.\ Therefore , \\\\[/tex]

[tex]\frac{3}{8} + \frac{1}{3} + \frac{1}{4} + x = 1\\\\\frac{9 + 8 + 6 + 24x}{24} = 1\\\\23 + 24x = 24\\24x = 1\\x = \frac{1}{24}[/tex]

[tex]On\ the\ fourth\ day\ he\ read\ \frac{1}{24} \ of\ the\ book\ to\ finish\ it.[/tex]

Help. I don't understand..

Answers

Answer:

3

Step-by-step explanation:

Answer:

75.4

Step-by-step explanation:

All angles in a triangle should equal 180, so the lil dash on K's side means angle K is the same as J

so 52.3+52.3=104.6

and 180-104.6 is 75.4

hope i helped and feel free to ask questions

in a class of 30 students the highest score in physics test was 98 and the lowest was 35 what was the range?​

Answers

Answer:

63

Step-by-step explanation:

basta ayon sagot ko obob ko eh

Graph a-7<-4


Will give brainlest

No links!!!!

Answers

Answer:

[tex]a\leq 3[/tex]

Step-by-step explanation:

[tex]a-7\leq -4,\\a\leq3[/tex]

When graphed, an arrow should be drawn pointing left with a solid dot on -3. Since the inequality line provided is not labelled, choose any vertical line and mark it as -3. Then add a solid circle and draw an arrow left, representing that the solutions of this inequality are all real numbers less than -3.

What is the length of the hypotenuse of the triangle when x=11​?

Answers

Answer:

hypotenuse = 93.06

Step-by-step explanation:

[tex]x = 11\\\\base = 4 \times 11 = 44\\\\height = 7x + 5 = 7 \times 11 + 5 = 77 + 5 = 82\\\\hypotenuse ^2 = base^2 + height^2\\[/tex]

                  [tex]=44^2 + 82^2\\\\=8660[/tex]

[tex]\\\\hypotenuse=93.06[/tex]

(X+4) • (3x)

(Help answer this )

Answers

Answer:

3x^2 +12x

Step-by-step explanation:

(x+4) • (3x)

Distribute

3x*x + 3x*4

3x^2 +12x

On a map, the distance between two towns is 12 centimeters. If 3 centimeters represents 90 miles, what is the actual distance between the cities in miles?

Answers

360 miles, I’m pretty sure

Find the following trigonometric values,rounded to 4 decimal places: 1) tan45. 2)sin70. 3) cos30. 4) cos20

Answers

1) Tan45 = 1
2) Sin70 = 0.9397
3) Cos30 = 0.8660
4) Cos20 = 0.9397

What do the following two equations represent? Y = -x + 5
5х + 5y = 20

Answers

Answer:

Letter B, distinct parallel lines

Step-by-step explanation:

I used a graphing calculator, tell me if it's correct.

A secretary works a 35-hour week for which she is paid $262.50. If in a particular week she works 6 hours overtime on Saturdays which is paid for at time - and - a - half and 4 hours overtime on Sunday which is paid for a double time. calculate her gross wage for that week​​


no links please​

Answers

Answer:

$390

Step-by-step explanation:

262.50/35 = 7.5 per hour during normal week

Saturdays  11.25 per hour

Sundays   15 per hour

6x11.25 = 67.5

4x15=60

   262.50 +67.5 +60 = 390

You already know I really don’t have to explain myself

Answers

Answer:

D

Step-by-step explanation:

Eddie needs to paint a fence which has 10,000 square feet of surface. One gallon of paint covers 600 square feet.
How many whole gallons of paint will he need?

Answers

Answer:

17

Step-by-step explanation:

10000/600=16.67

Please help me, I have trouble doing these type of questions.

Answers

Answer:

Bettina= X(let)

Darren=3x

Jonathan=6x

120=X+3x+6x

X=12

so Bettina=12 yrs

Darren=36 yrs

Jonathan=72 yrs

Answer:

Step-by-step explanation:

Let Bettina's age be B.

Then Darren's age is 3 times Bettina's, or 3B.

Jonathan's age is twice that of Darren, i.e. 2 (3B) = 6B.

Altogether, the sum of their age is

B + 3B + 6B  = 120 years

10 B = 120 years

B = 12 years.

Therefore

Bettina is 12 years old

Darren is 3 times as old as Bettina, so 36 years old.

Jonathan is twice that of Darren, so 72 years old.

Total = 72+36+12= 120 years, check!  :)

2) La expresión 7∙7∙7∙7 es igual a:
a) 47
b) 4+7
c) 47
d) 74

Answers

d) 7^4
because 7•7•7•7 is 7 to the power of 4

Answer:

d) 7⁴

Step-by-step explanation:

7 ∙ 7 ∙ 7 ∙ 7

cuatro sietes = siete elevado a cuatro

d) 7⁴

Which of these are factors of 16?
In geometry

Answers

Answer:

in geometry to find the factors of 16 we have to find numbers that can divide and without a number remaining 1,2,4

Based on the table,what is the volume,in litters,of sample 2?​

Answers

0.65 / 0.5 = 5.2 / ?

1.3 = 5.2 / ?

? = 5.2 / 1.3

? = 4 Liters

How do this I can’t do it?

Answers

Answer:

scale factor = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, scaled copy to original

scale factor = [tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex]

Simplify cos 0 csc 0.
a. cos 0
b. cot 0
c. tan 0
d. sin 0
Please select the best answer from the choices provided A B C D

Answers

Answer:

b cot

Step-by-step explanation:

csc= 1 over sin

so

cos x  1    =  cos  =  cot

 1      sin      sin

This question is worth 20 points and I will mark brainliest
which expressions are equivalent to 2 (3h + 7) choose "equivalent" or "Not equivalent" for each expression.


6h+7

2+3h+7

6h+7+7

3h+3h+14

(3h+7) + (3h+7)

Answers

Answer:

2(3h+7)

=6h+14

6h+7+7 (True)

3h+3h+14 (True)

estimate a 15% tip for a 19.80 meal.

Answers

the tip would equal $ 2.97.

19.80 x 0.15 = 2.97

Answer:

$3.00

Step-by-step explanation:

The tip would equal to $2.97 so the answer is $3.00 that is your estimate

find the circumference of a circle with a radius of 2.5 cm

Answers

C=2*pi*r
2*3.141592654*2.5
Answer: 15.7 cm

A tool box has the dimensions of 10 in by 4 in by 7 in. If Magnus plans to double all three dimensions to build a larger tool box, he believes he would double the volume of the tool box. Is he correct?

Answers

Answer: No. He's wrong.

Step-by-step explanation:

Since the tool box has the dimensions of 10 in by 4 in by 7 in. The volume will be:

= 10 × 4 × 7

= 280in³

When the dimensions are doubled, the new dimensions will be:

10 in = 10in × 2 = 20in

4in = 4in × 2 = 8 in

7in = 7in × 2 = 14in

The volume will now be:

= 20 × 8 × 14

= 2240in³

He is wrong, the volume isn't the double of the former tool box. The double of the former tool box will give (280in³ × 2) = 560in³. This is different from the new volume.

question in photo. i'll give brainliest to whoever gets it right/done quickest. thank you!

Answers

Answer:

Daniel's time: 3 minutes 45 seconds

Brandon's time: 3 minutes 27 seconds

Step-by-step explanation:

Well, 5 feet per every second so side A would be 327.6 / 3 = 109.2

then 489 / 5 = 97.8 add them two you get 207 seconds which is 3 minutes and 45 seconds for  Daniel.

For Brandon you have to find the hypotenuse of the triangle which in short is 588.6 / 3 = 196.2

This was my first answer on this so though Its problebly not the best I hope I did something to help. ;-;

The Martinez family picked 3 lb of apples. Ana picked for those apples,

How many pounds of apples did Ana pick?

Answers

Answer:

C. 7/8

Step-by-step explanation:

The Martinez family picked 3 and one-half pounds of apples. Ana picked one-fourth of those apples. How many pounds of apples did Ana pick?

options

A. 1/4

B. 3/4

C. 7/8

D. 1 1/4

E. 3 1/8

Total apples the Martinez family picked = 3 1/2 pounds

Ana picked one-fourth of those apples.

Number of apples Ana picked = 1/4 × 3 1/2 pounds

= 1/4 × 7/2 pounds

= (1 * 7) / (4 * 2) pounds

= 7/8 pounds

Ana picked 7/8 pounds of apples

Given the equation ab= c where a=2.
Select an equation that is equivalent.

A. ax2=c
B. bx2=c
C. cxa= b
D. b x C = a

Answers

The answer is B you can see my steps

Jorge has saved $15.50. Janet saved 15 of the amount that Jorge saved. Rob saved 12 times as much as Janet. What is the total saved amount of all three?

Answers

Answer: 45.725 ( i think)

Step-by-step explanation: 2.325 + 27.9 + 15.50

45.725 is the answer
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