Volume and Surface Area Find the surface area of the swimming pool.

Question

A swimming 20 m wide by 70 m long, 1 m deep at the shallow end and 3 m deep at the other end.  Find the total surface area of the pool.

Answer 1

Find the volume :

Volume V = length * width * average depth.

V = 20 * 70 * (1 + 3)/2

V = 20 * 70 * 2

V = 2800 m³

V = 2800 * 1000 L = 2800000 L.                    [since 1 m³ = 1000 L]

Volume of the swimming poool is 2800000 L.

----------------------------

Find the Surface  area of pool :

1m shallow at one end 3m deep at other end ,they are parallel sides.

Caliculate area of trepizium = 1/2(a+b)*h.

Length side area = 2 sides ( they are trapeziums )

Parallelsides are 1m, 3 m and perpendicular distance is 70 m.

= 1/2*(3+1)*70 = 140 m^2

Length side area , A1 = 140*2 = 280

Second side area, A2 = 20*1 = 20m^2

Third side area , A3 = 20*3 = 60m^2

Bottom surface = the distance along the length of pool from 1m depth to 3m depth.

From the pythagoras theorem the length is √70^2+2^2 = √4904 = 70.02 m

width = 20 m

Area of the base, A4 = 20*70.02 = 1400.4 m^2

Total surface  area , A = A1 + A2 + A3 + A4

                                 = 280+20+60+1400.4

                                  = 1760.4 m^2

Surface  area of pool is 1760.4m^2.