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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
 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
 one year ago

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

zepdrixBest ResponseYou've already chosen the best response.2
dw: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. \[\large A=2\pi r^2+2\pi r h \qquad \rightarrow \qquad A=2\pi\left(\dfrac{1}{3}h\right)^2+2\pi\left(\dfrac{1}{3}h\right)h\]
 one year ago

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

zepdrixBest ResponseYou've already chosen the best response.2
From 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.
 one year ago

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

zepdrixBest 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. \[\large 402=2\pi\left(\dfrac{1}{3}h\right)^2+\color{royalblue}{\dfrac{2\pi}{3}h^2}\]
 one year ago

zepdrixBest 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,\[\large 402=\color{#CC0033}{\dfrac{2\pi}{9}h^2}+\dfrac{2\pi}{3}h^2\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.2
We 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,\[\large 402=\dfrac{8\pi}{9}h^2\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.2
To 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,\[\large h^2=\dfrac{9\cdot402}{8\pi}\]
 one year ago

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

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