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標題:

f.3 math question

發問:

In the figure, a solid wooden sphere of radius r cm is to be cut into a cube of side 3 cm. Find the smallest possible value of r. Thank you for helping.

最佳解答:

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consider a cube,ABCDEFGH, ABCD is the base of cube we are looking. let X be the centre of the square,ABCD. AX = XB (AX)^2 + (XB)^2 = AB^2(Pytha.theo) 2XB^2 = 3^2 XB = 3/[(2)^1/2] Let O be the centre of the sphere. OX = 3/2 OB^2 = OX^2 + XB^2(pytha.theo) OB^2 = (3/2)^2 + 9/2 OB^2 = (9/4) + (9/2) OB^2 = 27 / 4 OB = [3(3)^1/2] / 4 OB = r the smallest radius is [3(3)^1/2]/4 cm

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