The uniform vertical cross-section PQRST of a swimming pool of length 50m and width 12m. The deepest point S of the cross-section is vertically below the point V. The areas of the cross-section PVST and VQRS are equal and PT = 1m, VS = 6m and QR = 2m.

(a)Given that VQ = x m, show that x = 23.3m, correct to one decimal place.

Calculate the volume of water in the pool, correct to 4 significant figures,

(b)when it is completely full;

(c)when the whole of the surface of the base of the pool is just covered with water.

(d)The pool is empty and is then filled by water flowing at a rate of

2.75 ms-1 through a system of 10 cylindrical pipes. Given that the radius of the cross-section of each of the pipes is r cm, write down an expression in terms of r and for the volume, in m3, of water flowing into the pool each hour through the system of pipes. Given that it takes 16 hours to fill the pool completely, calculate the value of r in cm, correct to 2 decimal places.

Im really confused to how i attempt this. Thanks