Frozen Ball

Geometry Level 4

A ball was floating in a lake, when the lake froze the ball was removed (without breaking the ice) having a hole 24 24 cm across at the top and 8 8 cm deep. Find the radius of the ball(in cm) .


The answer is 13.

Mietantei Conan by mietantei conan , 24, India

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2 solutions

Dhinesh Ganesan
Jul 21, 2014

frozen ball frozen ball

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Your soln is nt visible

Akarsh Kumar Srit - 5 years, 4 months ago
Ron Gallagher
Aug 16, 2019

Let x be the perpendicular distance from the center of the ball to the line (let's call the line L) where the ball is submerged. Then, if R is the radius, we see that x + 8 = R (because L is given to be 8 units from the bottom of the ball). However, L has length of 24 units (given), which means that 1/2 of the length of L is 12. An application of the Pythagorean Theorem then shows that x^2+12^2 = R^2. But, since R = x+8, this means that x^2+12^2 = (x+8)^2. Simplifying yields x = 5, so that R = x+8 = 5+8 = 13.

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