Maths(area and volume)

amy

2011-01-31 7:03 am

The figure shows a frustum ABCD of a right circular cone VBC.The radii of the upper base and the lower base are 2cm and3cm respectivel.The height of the frustum is 3cm.
a)Find VP
圖片參考：http://imgcld.yimg.com/8/n/HA00772322/o/701101300127713873375650.jpg

更新1:

點解5係 VP VD ----- = ------ ，VP：PQ，VD：CD ？ PQ CD

回答 (1)

Godfrey

2011-01-31 2:08 pm

✔ 最佳答案

Consider triangle VPD and triangle VQC
They are similar triangles because they have same internal angles. (90º, angle C and angle PVD)

Using ratio

VP VQ
----- = ------
PD QC

Let VP = x cm and VQ = VP + PQ

x x + 3
----- = ------
2 3

3x = 2(x + 3)
3x = 2x + 6
3x - 2x = 6
x = 6

VP = 6 cm

2011-02-03 21:47:33 補充：
To Amy:

PQ // QC
angle VDP = angle VCQ (corresponding angles)
tan angle VDP = tan angle VCQ (trig. function )
So VP/PD = VQ/QC

Godfrey

2011-02-03 21:55:44 補充：
Sorry, typo error in 意見:

PD // QC (not PQ // QC)

Alternatively, triangle VPD is similar to triangle VQC
Using ratio, VP/PD = VQ/QC

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