Geometry Question:help:

[Joey]

I'm helping my son with his homework , which is....How to find the volume of a cone....my son can find the V of every other shape but a cone...

If a cone has a diameter of 12 and a height of 12 what is it's volume?

( note: '' is my way of writing to the second power and ''' means cubed )

Here is the formula for finding the V of a cone...

V= 1/3πr''h

Or with this problem , since 12 is the diameter the radius is 6....so...here's this problem...

V= 1/3π (6)''(12)

So you need to multiply pi by 1/3 then multiply that by 6 and then that answer by 12....does anyone know if that is correct?

If not can someone tell us the correct way?

I think I figured it out...but any in put is helpful....

[Musky]

1809.5573684677208 ?

[Qapla]

V_c=1/3*pi*r²*h

V_c=Volume of Cone

pi=3.1416

r=radius (one-half the base)

h=height

So, in your question using your values:

V_c=1/3*pi*r²*h

V_c=1/3*pi*6²*12

V_c=1/3*pi*36*12

V_c=1/3*pi*432

V_c=1/3*3.1416*432

V_c=1/3*1357.1712

V_c=1357.1712÷3

V_c=452.3904

BTW - Here is a Volume of a Cone calculator that you can use to check your answers if he has more problems to solve. The results will vary a bit from my equation since I used pi=3.1416 and they use pi = 3.141592653589793

[trottigy]

452.16.

Remember the math order do the exponents first 6x6. Then the multiplication. It doesn't matter which you multiply together - the answer is the same.

36x12=432

432x 3.14=1356.48

Divide by 3 = 452.16

Or I could have divided any by 3 AFTER the exponent operation of 6x6. Then multiply together 36x4 which is 12/3 then x 3.14 = same 452.16

Note: if I use the pi key (3.14159265...) I get 452.389

Book is wrong. Try another check the answer.

[Qapla]

I didn't have a pi key, but if you want greater accuracy you could use

pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679

82148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428

81097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700

66063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657

59591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656

64308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082

77857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640

34418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308

25334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388

23537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818

27968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855

88907509838175463746493931925506040092770167113900984882401285836160356370766010471018194295559619894676

78374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935

11253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555

70674983850549458858692699569092721079750930295532116534498720275596023648066549911988183479775356636980

74265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573

52552133475741849468438523323907394143334547762416862518983569485562099219222184272550254256887671790494

60165346680498862723279178608578438382796797668145410095388378636095068006422512520511739298489608412848

86269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908

6583264599581339047802759009

[Joey]

452.16.

Remember the math order do the exponents first 6x6. Then the multiplication. It doesn't matter which you multiply together - the answer is the same.

36x12=432

432x 3.14=1356.48

Divide by 3 = 452.16

Or I could have divided any by 3 AFTER the exponent operation of 6x6. Then multiply together 36x4 which is 12/3 then x 3.14 = same 452.16

Note: if I use the pi key (3.14159265...) I get 452.389

Book is wrong. Try another check the answer.

I got 452.16....my husband who made straight A's in all his math courses did it and got 452.16.

[Joey]

V_c=1/3*pi*r²*h

V_c=Volume of Cone

pi=3.1416

r=radius (one-half the base)

h=height

So, in your question using your values:

V_c=1/3*pi*r²*h

V_c=1/3*pi*6²*12

V_c=1/3*pi*36*12

V_c=1/3*pi*432

V_c=1/3*3.1416*432

V_c=1/3*1357.1712

V_c=1357.1712÷3

V_c=452.3904

BTW - Here is a Volume of a Cone calculator that you can use to check your answers if he has more problems to solve. The results will vary a bit from my equation since I used pi=3.1416 and they use pi = 3.141592653589793

Thanks John....I won't show Sam that calculator but I'll use it. So I am doing the problems wrong , in some way? Can you explain?

[Joey]

New problem ...if you want to try it....

Question....

Cone volume for a cone 20 feet in diameter and 30 feet high.

The School math book and the calculator John posted have a slightly different answer....enough that Sam would have it marked as incorrect on a test.

[Trey]

V= 1/3π (6)''(12)

So you need to multiply pi by 1/3 then multiply that by 6 and then that answer by 12....does anyone know if that is correct?

If not can someone tell us the correct way?

I think I figured it out...but any in put is helpful....

You forgot to square the six before you multiplied. Otherwise you would have had it.

As Jerry mentioned, order of operations says to calculate your exponents before you multiply.

[Joey]

V= 1/3π (6)''(12)

So you need to multiply pi by 1/3 then multiply that by 6 and then that answer by 12....does anyone know if that is correct?

If not can someone tell us the correct way?

I think I figured it out...but any in put is helpful....

You forgot to square the six before you multiplied. Otherwise you would have had it.

As Jerry mentioned, order of operations says to calculate your exponents before you multiply.

OK. Thanks.

[Qapla]

...The School math book and the calculator John posted have a slightly different answer....

What answer did the math book have. If you use pi=3.14 you will get 452.16. The further you extend pi, the more the answer will "adjust" (see below)

Since his grade depends on it, use the value of pi the teacher/book uses.

pi=3.14 ... 452.16

pi=3.14159 ... 452.38896

pi=3.14159265 ... 452.3893416

pi = 3.141592653589793 ... 452.3893421169302

pi=3.1416 ... 452.3904

[Qapla]

BTW - maybe someone can "edit" my post with the extended pi since it is pushing all the buttons way off the screen

[Joey]

Hi John , the book answer is 452.389....I emailed the teacher because the book explained they were to use pi ...3.14....my husband was really irritated ,he said "I can't help him with this!"

So normally I am not the math homework helper....his book gives the answer to all the odd problems in the back.

He got a 50% on his quiz Friday....all the ones he got wrong were the cone volume questions.I asked if she could reset the test.Let him try those again once he knows how they want them done.

[tekmantwo]

Volume of a cone?

Easy!

FULL, please---

[Joey]

Volume of a cone?

Easy!

FULL, please---

And triple chocolate chunk!

[GrumpysWife]

Yummie!!!!!

[Just Bill]

Have him memorize the algebraic order of operations and the properties of addition, multiplication, subtraction and division.

 

I've used ^2, ^3 and so on before. I'm not sure if they are the "official" notation, but people seem to understand them well enough and they are relatively easy to understand.

 

My biggest epiphany came when I realized that there is only one basic math operation - addition - (using either positive or negative numbers) and that all the rest are simply variations on that theme.

 

That said, I never got to calculus so my understanding might not hold true there. As a die-maker, all of my math had to ultimately resolve to real numbers that I could measure directly or otherwise prove.

[Joey]

Thanks, I appreciate your suggestions.He had a 2 hour state profiency test yesterday,there was only 1 cone volume question on it, no other shape volumes mostly surface areas,etc. He thinks he did well.