Question

Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using city water at a rate of $3.95 per 100 gallons of water.


Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a water delivery service at a rate of $200 per 6000 gallons.


If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state who paid more to fill her pool. [ 1 ft3 water = 7.48 gallons]

Answer 1

Answer:

Step-by-step explanation:

Both pools were filled 6 inches from the top.

12 inches = 1 feet

6 inches = 6/12 = 0.5 foot

Considering Theresa's pool, it is rectangular. The formula for determining the volume if the rectangular pool is

Volume = length × width × height

Height filled is 4 - 0.5 = 3.5 feet

Volume = 30 × 15 × 3.5 = 1575 ft³

Recall, 1 cubic feet = 7.48 Us gallons

Therefore,

1800 cubic feet = 1575 × 7.48 = 11781 gallons of water

Theresa fills her pool using city water at a rate of $3.95 per 100 gallons of water. It means that the amount she paid to fill her pool is

3.95 × 11781/100 = $465.35

Considering Nancy's pool, it is cylindrical. The formula for determining the volume if the cylindrical pool is

Volume = πr²h

Diameter = 24

Radius = diameter/2 = 24/2 = 12 ft

Volume = 3.14 × 12² × 3.5 = 1582.56 ft³. Converting to gallons, it becomes

1582.56 × 7.48 = 11837.55 gallons of water.

Nancy fills her pool with a water delivery service at a rate of $200 per 6000 gallons.

It means that the amount she paid to fill her pool is

200 × 11837.55/6000 = $394.59

Therefore, Theresa paid more to fill her pool.