[填空题]
The cross-sectional view of a tw 9 /p,k6we 67be ,gmcqwqcstp*o-lane road tunnel system is show.y1d3 w- blocl:vea(d n on the axes below. The left and right lane tunn:3(db1ed lclyv.o- awels are separated by a 2 metre thick concrete wall. The right-hand tunnel passes through the points A, B, C and D and its height, in metres, above the base of the tunnel, is modelled by
$ f(x)=-0.04 x^{3}+0.41 x^{2}, 4 \leq x \leq 10$ , relative to an origin O .
Point A has coordinates (4,4) and point $ \mathrm{D} $ has coordinates (10,1) .
1. Find the height of the right-hand tunnel when:
1. x=6 ;f(6)= .
2. x=8 .f(8)= .
The left-hand tunnel can be modelled by a function g(x) , found by reflecting f(x) in the line x=3 .
2. Find the equation of g(x) .
3. 1. Find $g^{\prime}(x)$ .
3.2. Hence find the maximum height of the left-hand tunnel.The maximum height of the left-hand tunnel is approximately m.
4. 1. Write down an integral which can be used to find the cross-sectional area of the left-hand tunnel.
2. Hence find the combined cross-sectional area of both tunnels.
The combined cross-sectional area of both tunnels is approximately m$^2$.
