F.3 Maths(HELP)

[匿名]

2011-06-19 4:49 am

1.In the figure, ABCD is a parallelogram. Find the length of BD.BFE and BDC are similar Triangles.

圖片參考：http://imgcld.yimg.com/8/n/HA00115843/o/701106180103513873460780.jpg

2.
In the figure, the top and the base of the right frustum are squares of side a and 6a respectively. if the height of the original right pyramid is h. Find the ratio of
volume of frustum to volume of the original pyramid
圖片參考：http://imgcld.yimg.com/8/n/HA00115843/o/701106180103513873460791.jpg

回答 (1)

Godfrey

2011-06-20 9:35 am

✔ 最佳答案

Question 1:
BC = AD = 13 (opposite side of a parallelogram is equal.
BC/BE = BD/BF
13/6 =BD/4
BD = (13/6)(4) = 52/6 = 8.6667
BD = 8.6667 (accurate up 4 decimal place)

Question 2:
Volume a square pyramid is given by
1/3 (s^2)h where s = side length of base, h = height
Volume of small pyramid AFGHJ = 1/3(a^2)h
Volume of large pyramid ABCDE = 1/3((6a)^2)6h = 1/3(36a^2)6h = 1/3[(216a^2) h]
Volume of Frustrum = Vol. of large pyramid – Vol. of small pyramid
Volume of Frustrum = 1/3[(216a^2) h] - 1/3(a^2)h = 1/3 a^2 h(216 – 1) = 215/3 a^2 h
Ratio of volume of frustum to volume of the original pyramid
= (215/3 a^2 h)/ 1/3(a^2)h
= 215/1
Ratio of volume of frustum to volume of the original pyramid is 215 to 1.

It is assumed that original pyramid is the small pyramid because the height of original pyramid is h. (given)

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