Fun with 2018 #6

Geometry Level 1

The biggest volume V V of a cone inscribed in a sphere of radius 2018 2018 can be written as V = 1 3 π ( 201 8 2 − x 2 ) ( 2018 + x ) V = \frac{1}{3} \pi (2018^2 - x^2)(2018 + x) where x = A B ⋅ 2018 x = \frac{A}{B} \cdot2018 with A , B A, B coprime positive integers. Enter 10 A + B + 5 10A + B + 5 .


The answer is 18.

Guillermo Templado by Guillermo Templado , 46, Spain

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1 solution

Saya Suka
Jan 20, 2021

It's like how a largest tetrahedron is placed in a sphere, the central point distance from the peak is triple of that from the bottom face.
Answer
= 10(1) + (3) + 5
= 18


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