[问答题]
A water truck tank which is 3 metres long
97 9(2so zvv*jrcpylx has a uni
4o ,g 1yh6)d-4s woykants+zkrntb5*form cross-section in the shape of a major segment. The tank is divided into two equal parts and is partially filled with water as shown in the follo
1wtsr n+-yso o* 56k 4gh4zy)ak,tnbdwing diagram of the cross-section. The centre of the circle is O , the angle AOB is $\alpha$ radians, and the angle AOF is $\beta$ radians.
1. Given that $\alpha=\frac{\pi}{4}$ , calculate the amount of water, in litres, in the right part of the water tank. Give your answer correct to the nearest integer.
2. Find an expression for the volume of water V , in $ \mathrm{m}^{3}$ , in the left part of the water tank in terms of $\beta$ .
he left part of the tank is now being filled with water at a constant rate of 0.001 $\mathrm{~m}^{3}$ per second.
3. Calculate $\frac{\mathrm{d} \beta}{\mathrm{d} t}$ when $\beta=\frac{3 \pi}{5} $. Round your answer to 3 significant figures.
4. Calculate the amount of time it will take for the left part of the tank to be fully filled with water. Give your answer in minutes and correct to the nearest integer.
