更新1:
The height is a constant .
更新2:
a positive non-zero constant
更新3:
Ans. 8 cm
differentiation
2012-03-21 7:30 am
If the right cylinder with its greatest curved surface area is inscribed in a right circular cone of radius 16 cm , find the radius of the cylinder.
回答 (2)
2012-03-21 6:16 pm
✔ 最佳答案
As the height is a constant, asuume H. Let the height and the radius of the cylinder be h, r respectively.The curved surface area (S) of the cylinder is :
2πrh
= 2πr(16 - r)*(H/16) . . . . (Using the ratio of similar △)
= (πH/8)(16r - r^2)
As S = (πH/8)(16r - r^2)
dS/dr = (πH/4)(8 - r)
When dS/dR = 0, r = 8
So, when the radius of the cylinder is 8cm, its curved surface area is the greatest.
2012-03-21 3:29 pm
What is the height of the cone ? 10 cm.? 100cm.? 10000 cm.?......
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