If the sector shown in the figure is made into a conical vessel by joining OA and OB,find the a)base radius and b)the capacity of the vessel.
圖片參考：http://imgcld.yimg.com/8/n/HA00772322/o/701102030055013873376840.jpg
I know the answer is 4.5cm.Please explain to me why.Can i write108/360x15,because the answer of 108/360x15 is 4.5m
Maths(measures,shape,space)
2011-02-04 2:42 am
回答 (1)
2011-02-04 3:24 am
✔ 最佳答案
Since the base of conical vessel is made by joining A and B, so the length of circumference of the base is the length of arc AB.a)
Length of arc AB=(108°/360°)*2π(15)=9π cm
We let the radius be r:
2πr=9π
r=9/2 cm
b)
Height of the vessel=√[15^2-(9/2)^2]=√819/2
The capacity of the vessel
=(1/3)*base area*height
=(1/3)*π(9/2)^2*√819/2
=(27√819)π/8
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