Gina stores her toys in a container which has a cylindrical body and a conical lid, as shown below.
She wants to cover the entire exterior portion of the container with paper. How much paper, in square feet, would Gina need?
28 π
16π
20π
24 π
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OpenStudy (anonymous):
OpenStudy (anonymous):
tips?
OpenStudy (kinggeorge):
Do it one step at a time. What's the surface area of the cylinder? (not including the base)
OpenStudy (anonymous):
hmm
OpenStudy (anonymous):
3 pi plus pi?
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OpenStudy (anonymous):
cause (pi)(r)(h) + (pi)(r squared)
OpenStudy (anonymous):
3pi +pi
OpenStudy (anonymous):
4 pi
OpenStudy (kinggeorge):
First, \(r=2\).
Second, it's \(2\pi r h+\pi r^2\).
OpenStudy (anonymous):
ahh
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OpenStudy (anonymous):
12 pi +4 pi
OpenStudy (anonymous):
16 pi
OpenStudy (anonymous):
2 times 2
OpenStudy (anonymous):
4 pi
OpenStudy (kinggeorge):
Right. Now we need to find the surface area of the cone at the top. Do you know the formula for this?
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OpenStudy (anonymous):
2 times 2
OpenStudy (anonymous):
4 pi + 4 pi + 16 pi=24 pi
OpenStudy (anonymous):
24 π
OpenStudy (anonymous):
right?
OpenStudy (kinggeorge):
Why do you have two \(4\pi\)'s in there?
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OpenStudy (anonymous):
well
OpenStudy (anonymous):
the surface area of the cone is 8 pi
OpenStudy (anonymous):
so 8 pi +16 pi=24 pi
OpenStudy (anonymous):
and
OpenStudy (anonymous):
pi(2)(2) plus pi(2 squared)
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OpenStudy (kinggeorge):
Explain to me where you got the 8pi from. Remember that we don't include the base of the cone since it's contained within the solid.
OpenStudy (anonymous):
ehh
OpenStudy (anonymous):
so its 20 pi
OpenStudy (anonymous):
so yo udon't apply the whole suface area
OpenStudy (anonymous):
so its pi(r)(l)
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