Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
julianahe
Group Title
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
julianahe Group Title
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

This Question is Closed

julianahe Group TitleBest ResponseYou've already chosen the best response.0
plz helppp!! i
 one year ago

klimenkov Group TitleBest 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

julianahe Group TitleBest ResponseYou've already chosen the best response.0
SA= 2πr^2 + 2πrh
 one year ago

zepdrix Group TitleBest 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

zepdrix Group TitleBest 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

zepdrix Group TitleBest 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

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

zepdrix Group TitleBest 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

zepdrix Group TitleBest 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

zepdrix Group TitleBest 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

zepdrix Group TitleBest 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

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

zepdrix Group TitleBest 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

julianahe Group TitleBest ResponseYou've already chosen the best response.0
Ok thank you!!
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.