设圆锥的高为h1米,母线长为l米,圆柱的高为h2米;
(1)∵圆锥和圆柱的总高度和圆柱底面半径相等,都为r米.
则h1<r,
tanθ=
h1 |
r |
∴θ∈(0,
π |
4 |
(2)圆锥的侧面用料费用为4aπrl,圆柱的侧面费用为2aπrh2,圆柱的地面费用为2aπr2,..(6分)(每个面积公式1分)
则y=4aπrl+2aπrh2+2aπr2
=2aπr(2l+h2+r)=2aπr[
2r |
cosθ |
=2aπr[
2r |
cosθ |
2 |
cosθ |
(3)设f(θ)=
2 |
cosθ |
π |
4 |
则f′(θ)=
2sinθ-1 |
cos2θ |
当θ=
π |
6 |
2sinθ-1 |
cos2θ |
当θ∈(0,
π |
6 |
2sinθ-1 |
cos2θ |
当θ∈(
π |
6 |
π |
4 |
2sinθ-1 |
cos2θ |
则当θ=
π |
6 |
则当θ=
π |
6 |