Diamonds Posted August 11, 2013 Posted August 11, 2013 (edited) 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
SshinigamiS Posted August 11, 2013 Posted August 11, 2013 (edited) 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 1
Baller Posted August 11, 2013 Posted August 11, 2013 (edited) A. Keep ur 100k Edited August 11, 2013 by Zeei
MoneyMan Posted August 11, 2013 Posted August 11, 2013 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 Posted August 11, 2013 Posted August 11, 2013 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 Posted August 11, 2013 Posted August 11, 2013 (edited) nevermind...messed up lol Edited August 11, 2013 by ihavecoolhats
ohhungry Posted August 11, 2013 Posted August 11, 2013 (edited) 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 1
