Question #206011

Four grapefruit (considered spheres) 6

in. in diameter and place in a square box whose inside base dimensions are 12

in. in the space between the first four grapefruit a fifth of the same diameter is placed. How deep must the box be so that the top will just touch the fifth grapefruit?

Expert's answer

Solution

A,b,c,D,E is the center of the grapefruit ..

So "AB=BC=CD=AD=BE=CE=b"

ABCD is a square

"OC= \\frac{AC}2\\space BC=3\\sqrt{2}"

"h_1= \\sqrt{EC^2-OC^2}=\\sqrt{36-18}=b\\sqrt{2}"

"So \\space h=r+h=\\frac{1}2 *6+ 3 \\sqrt{2}+ \\frac{1}2*6"

"=6+3 \\sqrt{2} \\space in"

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