Math Challenge # 2 - 100k winner

[Diamonds]

WINNER - ohhungry

Who ever answers this question fully detailed and explains it from scratch will win 100k. Contest will end in 1 hour so try to explain the best.

 

What is the radius of a Cylinder if the volume is 300cm^3, and the height is 10 cm?

 

A. 3.1 CM

B. 9.5 CM

C. 4.7 CM

D. There is not enough info.

Edited August 11, 2013 by Diamonds

[udeme123]

ain't nobody got time fo dat

[MoneyMan]

D. Keep your money.

[Diamonds]

D. Keep your money.

incorrect.

[SshinigamiS]

Area of a circle: Pi x r^2. (Pi r squared)

 

Volume of a cylinder = 300cm^3.

 

300cm^3 = Height x Pi r ^2.

 

We know the height is 10cm.

 

300cm^3 = 10cm x Pi®^2

 

Divide both sides by 10cm.

 

30cm^2 = Pi®^2

 

30cm^2 divided by Pi = r^2

 

9.549296586... = r^2

 

Square root both sides.

 

3.090193616... = Radius.

 

= 3.1 to 1 d.p

 

Keep the 100k, you're welcome

 

Answer = 3.1cm.

Edited August 11, 2013 by SshinigamiS

[Baller]

A. Keep ur 100k

Edited August 11, 2013 by Zeei

[MoneyMan]

The answer is A if you devide 300cm by the height which is 30cm. 30cm / PI which is 9.6, so square root of 9.6 is 3.1cm

[MoneyMan]

Area of a circle: Pi x r^2. (Pi r squared)

 

Volume of a cylinder = 300cm^3.

 

300cm^3 = Height x Pi r ^2.

 

We know the height is 10cm.

 

300cm^3 = 10cm x Pi®^2

 

Divide both sides by 10cm.

 

30cm^2 = Pi®^2

 

30cm^2 divided by Pi = r^2

 

9.549296586... = r^2

 

Square root both sides.

 

3.090193616... = Radius.

 

= 3.1 to 1 d.p

 

Keep the 100k, you're welcome 

 

Answer is most definately = 3.1cm.

[Han Solo]

nevermind...messed up lol

 

 

 

 

Edited August 11, 2013 by ihavecoolhats

[Adriana]

                       2

Answer: E=MC

 

 

[Jordan]

[ohhungry]

We can do this with a simple triple integral and some algebra.

 

If you split the cylinder into very small circular slices, each of those slices would have a volume equal to (Area of Circle)*(Δh). To find the area of each circular slice, we can take the circle to be a series of concentric disks, each with a width Δr. Using polar coordinates, we can express the area of the circle as a double integral. Since each disk goes about a 360 degree rotation (or 2π) this will be our angle of integration, giving us the following integral: ∫(0-2π)∫(0-R)[rdrdθ]

 

We now take this integral, and integrate it over our height of 10cm, and this integral will be equal to the volume of the cylinder, which is 300cm^3

 

So our equation is:

 

300 = ∫(0-10) ∫(0-2π)∫(0-R)[rdrdθdh]

300 =10 (∫(0-2π)∫(0-R)[rdrdθ])

30 = 2π(∫(0-R)[rdr])

30 = 2π[(r^2)/2](0-R)

30=π(r^2)

sqrt(30/π) = r

r ~ 3.1

 

Therefore the answer is A) 3.1cm

Edited August 11, 2013 by ohhungry

[goosey1]

2e=mc