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Volume of frustum?

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發問:

A frustum ABCD with an upper radius 10 cm and a lower radius 8 cm. The length of CD is 8 cm. Find the height of the frustum (h) and volume of the frustum. corr. to 3 sig fig.

最佳解答:

(1) h2 + ( 10 - 8 )2 = 82 h2 + 4 = 64 h2 = 60 h = √60 = 2√15 ≒ 7.75 Ans : 7.75 cm (2) Suppose the center of the upper circle is O, AB and CD intersect at P. Let k = OP ( k - h ) : 8 = k : 10 10k - 10h = 8k 2k = 10h k = 5h = 5 * 2√15 = 10√15 V = (1/3)π(102)k - (1/3)π(82)( k - h ) = (1/3)π*100*10√15 - (1/3)π*64*8√15 = ( 1000/3 - 512/3 )π√15 = (488/3)π√15 ≒ 1980 Ans : 1980 cm3

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