maths question!!!!(mensuration)

digimon1225

2008-08-26 2:40 am

The figure shows a right circular cone with base radius 6 and height 15.
A cyclinder with height h and base radius r is inscribed in the circular cone.

if the volume of the cylinder is 2/9 of that of the circular cone,find the value of r.

p.s.(ans has two)

回答 (1)

用戶10012

2008-08-26 8:14 pm

✔ 最佳答案

By similar triangle, (15-h)/r = 15/6= 5/2. 2(15 -h) = 5r. 30 - 2h = 5r
Therefore, h = 5(6 -r)/2
Volume of cylinder = (pi)r^2h = (pi)r^2[5(6-r)/2]
Volume of cone = (1/3)(pi)6^2(15) = 180(pi).
Therefore, (pi)r^2[5(6-r)/2] = 180(pi)(2/9)
r^2[5(6-r)/2] = 40
r^2(6 -r) = 16
r^3 - 6r^2 + 16 = 0
(r -2)(r^2 -4r - 8) = 0
Roots of r^2 - 4r - 8 = 0 are 2 + sqrt(12) and 2 - sqrt(12) [rej.]
Therefore, r = 2 and 2 + 2sqrt2.

2008-08-26 12:16:03 補充：
Correction: answer should be 2 + sqrt3, not 2 + sqrt2, sorry.

2008-08-26 12:17:49 補充：
Correction: Again mistake! Answer should be 2 + 2sqrt3. in the last line.

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