anonymous
  • anonymous
Lab is to find the radius and height of a right circular cylinder where the surface area and volume are the same number. Is there a solution? Is there more than one?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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campbell_st
  • campbell_st
well the surface area is \[SA = 2\pi r^2 + 2\pi r h\] and the volume is \[V = \pi r^2 h\] so if they are equal to the same number \[\pi r^2 h = 2\pi r^2 + \pi r h\] and then work from there..
anonymous
  • anonymous
what should I choose for the number? any?
campbell_st
  • campbell_st
so if you have \[\pi r^2 h = 2 \pi r^2 + 2 \pi r h\] divide every term by \[\pi r\] then \[rh = 2r + 2h\] make h the subject \[h( r -2) = 2r\] then \[h = \frac{2r}{r + 2}\]

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campbell_st
  • campbell_st
that's my best guess at this question... so r > 0
campbell_st
  • campbell_st
so as r gets large it looks like h gets closer to 2...
anonymous
  • anonymous
ok thanks

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