math problem

3.
(a)
Area of the shaded region
= Area of the sector - Area of the triangle
= π * (6 cm)² * (60/360) - (1/2) * (6cm) * (6 cm) * sin60°
= 6π - 18 * (√3)/2 cm²
= 6π - 9√3 cm²

(b)(1)
The capacity of C
= (1/2) * π * (12/2 cm)² *(20 cm)
= 360π cm²
≈ 1131 cm² (to 4 sig. fig.)

(b)(2)
The cross-section of water is identical to the shaded region in figure 3(a).

Volume of water in C
= [(6π - 9√3) cm²] * (20 cm)
= (120π - 180√3) cm³
≈ 65.22 cm³ (to 4 sig. fig.)

(b)(3)
[(1/3) * π * (2 cm)² * (5 cm) * x] + (120π -180√3) ≥ 360π
(20/3)πx ≥ 360π - (120π - 180√3)
(20/3)πx ≥ 240π + 180√3
x ≥ (240π+ 180√3) * (3/20π)
x ≥ 50.89

The minimum value of x = 51

2014-06-02 22:04:32 補充：
(b)(3)
誤把 cylindrical 當作 conical，多乘了 1/3。正確答案是：

[π * (2 cm)² * (5 cm) * x] + (120π -180√3) ≥ 360π
(20)πx ≥ 360π - (120π - 180√3)
(20)πx ≥ 240π + 180√3
x ≥ (240π+ 180√3) / (20π)
x ≥ 16.96

The minimum value of x = 17

b(3) is wrong, my teacher told me that the answer is17. But I don't know the steps.