When three spherical balls, each of radius 10cm, are placed in a hemispherical dish, it is noticed that the tops of the balls are all exactly level with the top of the dish. What is the radius, in centimetres, of the dish?

Question

anonymous · Answer

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Something like this...

valpey · Answer

Awesome problem!!!

anonymous · Answer

haha thanks..i've gotten halfway but i don't know how to finish it...

valpey · Answer

Look at the cross sectional area of the plane going through the center of one of the balls. Because the balls are arranged in an equilateral triangle we can calculate the displacement of the center of a ball from the center of the bowl.

anonymous · Answer

yeh i did that and i got a final answer of 21.54 but i am pretty sure that this answer is wrong...

valpey · Answer

On the plane of the top of the bowl, the center of each ball is displaced $$10\frac{2}{\sqrt{3}}$$ and because the ball is tangent to the bowl, the radius of the bowl is collinear with the radius of the ball.

anonymous · Answer

yeh i got that bit... then i added 10 which is the radius of a sphere... but i think that is wrong.

valpey · Answer

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The Death Star!