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A cone is created by rotating an isosceles right triangle with leg length 2 about one of its legs. Its surface area is pi times what number?

RektTheNoob  Dec 6, 2017

Best Answer 

 #1
avatar+5576 
+1

Here is the triangle before it is rotated. We can imagine that it will be rotated about the gray line.

 

We can see that...

 

the radius of the cone's base   =   r   =   2

 

the height of the cone   =   h   =   2

 

the surface area of the cone   =   π r (r + \(\sqrt{h^2+r^2}\) )

 

the surface area of the cone   =   π (2) (2 + \(\sqrt{2^2+2^2}\))

 

the surface area of the cone   =   2π (2 + √8)

 

the surface area of the cone   =   2π (2 + 2√2)

 

the surface area of the cone   =   π (4 + 4√2)

hectictar  Dec 6, 2017
edited by hectictar  Dec 6, 2017
edited by hectictar  Dec 6, 2017
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1+0 Answers

 #1
avatar+5576 
+1
Best Answer

Here is the triangle before it is rotated. We can imagine that it will be rotated about the gray line.

 

We can see that...

 

the radius of the cone's base   =   r   =   2

 

the height of the cone   =   h   =   2

 

the surface area of the cone   =   π r (r + \(\sqrt{h^2+r^2}\) )

 

the surface area of the cone   =   π (2) (2 + \(\sqrt{2^2+2^2}\))

 

the surface area of the cone   =   2π (2 + √8)

 

the surface area of the cone   =   2π (2 + 2√2)

 

the surface area of the cone   =   π (4 + 4√2)

hectictar  Dec 6, 2017
edited by hectictar  Dec 6, 2017
edited by hectictar  Dec 6, 2017

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