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October 19th, 2014, 09:49 AM  #1 
Newbie Joined: Oct 2014 From: London Posts: 27 Thanks: 0  Calculate the radius of the cylinder if its height is 2.80m?
The total SA of a closed cylindrical container is 20.0cm^2. Calculate the radius of the cylinder if its height is 2.80m I know the SA formula is 2pir+2pirh=20cm but from here? 
October 19th, 2014, 10:45 AM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,878 Thanks: 1502  Quote:
$\displaystyle A = 2\pi r^2 + 2\pi r h $ sub in 2.8 for h and 20 for A ... solve for r  
October 19th, 2014, 10:52 AM  #3 
Newbie Joined: Oct 2014 From: London Posts: 27 Thanks: 0  
October 19th, 2014, 10:58 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,878 Thanks: 1502  
October 20th, 2014, 02:04 PM  #5 
Senior Member Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230 
$\displaystyle \textbf{Hello, mathsheadache (However, maths is not a headache.)}$ $\displaystyle \textbf{We know,}$ $\displaystyle \textbf{Total Surface Area of a cylinder}=2 \pi r(r+h)$ $\displaystyle \textbf{Here, TSA is given to be 20} \textbf{cm}^{2}$ $\displaystyle \textbf{Height = 2.80 m but we need to be consistent with units, so let's convert in cm.} $ $\displaystyle \textbf{So, h = 280 cm.}$ $\displaystyle \textbf{According to the question,}$ $\displaystyle 2 \pi r^{2} + 2 \pi r \times 280 = 20 \ \ \textbf{cm}^{2}$ $\displaystyle \textbf{Divide each term by}\ \ 2 \pi$ $\displaystyle r^{2} + 280r = 3.183$ $\displaystyle \textbf{Rearrange this into:}$ $\displaystyle r^{2} + 280r  3.183 = 0$ $\displaystyle \textbf{A quadratic equation can be solved in three ways :}$ $\displaystyle \textbf{1. By middletermsplitting method.} \\ \textbf{2. By completing the square.} \\ \textbf{3. By using the quadratic formula.}$ $\displaystyle \textbf{In this case, we use the Quadratic Formula :}$ $\displaystyle \textbf{A Quadratic Equation of the form } ax^{2}+bx+c=0 \ \ \textbf{can be solved by the following formula :}$ $\displaystyle x=b \pm \frac{\sqrt{b^{2}4ac}}{2a} \ \ \textbf{where x represents an unknown, and a, b, and c are constants with }a \neq 0$ $\displaystyle \textbf{If you solve that using the usual quadratic formula, the positive value for r is 0.01 cm.} $ $\displaystyle \textbf{Is the height = 2.80 m, or is it 2.80 cm?}$ $\displaystyle \textbf{If it is the latter, then :}$ $\displaystyle r^{2} + 2.8r  3.183 = 0$ $\displaystyle \textbf{would give:}$ $\displaystyle r = 0.868 \ \ \textbf{cm}$ Last edited by Prakhar; October 20th, 2014 at 02:22 PM. 
October 20th, 2014, 07:38 PM  #6  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
 

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280m, calculate, cylinder, height, radius 
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divide 80m by 20cm,2pirh formula,how we know that area of cylinder is 2pi rh,6,2,2,58 is an AP find the middle term ? how to solve,how to find radius in 2 pi rh,the total surface of a closed cylindrincal container is 20 m. calculate the radius of the cylinder,height=2.80m
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