# math

A rectangular pool's depth is 1m at the shallow end and gradually increases to 4m at the deep end. The pool is 32m in length and 12m width.

1. calculate the total surface area (m squared) of the pool.
2. The cost of painting the pool at \$5 per square foot.
3. the amount of water(litres) required to fill the pool.

1. SA is the rectangular base + 2ends + 2trapezpoids
for the length of the slanted base we need to use Pythagoras

H^2 = 32^2 + 3^2
h = √1033

area of base = 12√1033
area of each trapezoid
= 32(1+4)/2 = 80
short end = 12
deep end = 48

Total surface area = 12√1033 + 2(80) + 12 + 48
= 605.684 m^2

b) I will assume you meant \$5 per square metre
cost = 5(above surface area)

c) I will consider one of the traps as the base
Volume = 80(12) = 960 m^3
= 960 000 litres

posted by Reiny

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