Circumscribed triangle

Geometry Level pending

A right triangle with hypotenuse c = 2 ( 1 + 6 ) c = 2(1+ \sqrt{6} ) is circumscribed on a circle with unit radii. Find the surface area of the conical shape formed by the rotation of the right triangle around its biggest leg .

Note : if the answer is in the form π ( x y + z ) \pi (x \sqrt{y} + z) evaluate x + y + z x+y+z . And the expression leg is referred to be the non hypotenuse sides of a right triangle.


The answer is 26.

Relue Tamref by Relue Tamref , 21, Brazil

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1 solution

Relue Tamref
Aug 7, 2017

Very detailed geometric interpretation from the solution i hope you guys can understand my calligraphy.

Solving the system in red this gives us a = 4 + 6 , b = 6 a= 4 + \sqrt{6}, b= \sqrt{6} and then using the formula for conical shape surface we have:

S a = π 6 ( 6 + 2 + 2 6 ) = π ( 2 6 + 18 ) S_a = \pi \sqrt{6} ( \sqrt{6}+ 2 + 2 \sqrt{6}) = \pi (2 \sqrt6 + 18) so answer is 2 + 6 + 18 = 26 2+6+18=26

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