Answer to Question #206011 in Civil and Environmental Engineering for John

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? 


1
Expert's answer
2021-06-11T22:58:24-0400

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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