a) First of all, it is necessary to calculate the circumference of the pool.
You have the diameter is 24 feet.
Use the formula for the circumference of a circle:
C = 2πr
where C is the sircumference and r is the radius, which is one half of the diameter:
r = d/2 = 24 ft/2 = 12 ft
replace in the formula for C:
C = 2π(12) = 24π ft
The lining for the side of the pool is sold in six foot tall rolls that are 20 feet long.
To determine the required number of rolls. You divide the circumference of the pool between the length of the linings, just as follow:
24π/20 = 3.76
Hence, to cover the pool completely, the family need 4 rolls of lining (it has been approximated to the greater nearest integer because it is necessary to ensure the lining ot the complete pool).
b) The area of the cover is the area of a circle, then you use the following formula:
A = πr² = π(12 ft)² = 452.38 ft²
Hence, the are of the cover is 452.38 ft²
c) To determine the amount of water, it is necessary to use the formula for the volume of a cylinder, which is given by:
V = πr²h
In this case h is the height of the water inside the pool, which is equal to
6 ft - 0.5 ft = 5.5ft. You replace this value of h and the value of r in the formula for V:
V = π(12 ft)²(5.5ft) = 2,488.14 ft³
Hence, there are 2,488 ft³ of water in the pool.