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 one year ago
A cylinder has a surface area of 402 cm^2. The height is three times greater than the radius.
What is the height of the cylinder?
 one year ago
A cylinder has a surface area of 402 cm^2. The height is three times greater than the radius. What is the height of the cylinder?

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klimenkov
 one year ago
Best ResponseYou've already chosen the best response.0I will help you if you'll write a formula for the surface area for a cylinder.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2dw:1359238717297:dwThey told us that \(h=3r\), which we can rewrite as \(\dfrac{1}{3}h=r\). From here, we can substitute this \(h\) value in place of all the \(r\)'s in the formula. \[\large A=2\pi r^2+2\pi r h \qquad \rightarrow \qquad A=2\pi\left(\dfrac{1}{3}h\right)^2+2\pi\left(\dfrac{1}{3}h\right)h\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Then plug the value for surface area that they provided,\[\large 402=2\pi\left(\dfrac{1}{3}h\right)^2+2\pi\left(\dfrac{1}{3}h\right)h\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2From here it's just a few algebra steps to solve for h. Lemme know if you're confused by any of that, or need to see more steps.

julianahe
 one year ago
Best ResponseYou've already chosen the best response.0can u waalk me throught the whole thing? im having trouble solving

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2\[\large 402=2\pi \color{orangered}{r}^2+2\pi \color{orangered}{r} h \qquad \rightarrow \qquad 402=2\pi\color{orangered}{\left(\dfrac{1}{3}h\right)}^2+2\pi\color{orangered}{\left(\dfrac{1}{3}h\right)}h\]So we found or relationship with r and h and made the replacement. Now let's try to solve for h.\[\large 402=2\pi\left(\dfrac{1}{3}h\right)^2+\color{royalblue}{2\pi\left(\dfrac{1}{3}h\right)h}\]Let's work on the blue part first. \[\large 402=2\pi\left(\dfrac{1}{3}h\right)^2+\color{royalblue}{\dfrac{2\pi}{3}h^2}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2\[\large 402=\color{#CC0033}{2\pi\left(\dfrac{1}{3}h\right)^2}+\dfrac{2\pi}{3}h^2\]Now to simplify the red term, make sure you square both the h and the 1/3.\[\large 402=\color{#CC0033}{2\pi\left(\dfrac{1}{9}h^2\right)}+\dfrac{2\pi}{3}h^2\]Which simplifies to,\[\large 402=\color{#CC0033}{\dfrac{2\pi}{9}h^2}+\dfrac{2\pi}{3}h^2\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2We have a couple of fractions, let's get a common denominator, multiplying the second term by \(\dfrac{3}{3}\).\[\large 402=\dfrac{2\pi}{9}h^2+\color{#996666}{\dfrac{3}{3}}\cdot\dfrac{2\pi}{3}h^2\]Giving us,\[\large 402=\dfrac{2\pi}{9}h^2+\dfrac{6\pi}{9}h^2\]Adding these terms together gives us,\[\large 402=\dfrac{8\pi}{9}h^2\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2To get rid of the fraction on the right, we'll multiply both sides by it's reciprocal.\[\large \color{#662FFF}{\left(\dfrac{9}{8\pi}\right)}402=\dfrac{8\pi}{9}h^2\color{#662FFF}{\left(\dfrac{9}{8\pi}\right)}\]We can cancel the fractions on the right,\[\large \color{#662FFF}{\left(\dfrac{9}{8\pi}\right)}402=\cancel{\dfrac{8\pi}{9}}h^2\cancel{\color{#662FFF}{\left(\dfrac{9}{8\pi}\right)}}\]Giving us,\[\large h^2=\dfrac{9\cdot402}{8\pi}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Punch that number into your calculator, and take the square root, and voila!!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Sorry if that was too slow, I like to add the colors. I think they make it a little easier to read.
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