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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 numb

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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?

Dec 6, 2017

#1
+7348
+2

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)

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

#1
+7348
+2

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