Question

the summer hotel is installing a new pool. the pool will be rectangular in shape, with a depth of 10 feet, as shown in the diagram. at one end of the pool, there will be a shallower entrance, with a depth of 4 feet, in the shape of a half - cylinder. complete all parts of the task to help the hotel plan for the pool installation. question part a the hotel needs to apply a non - slip paint finish to the interior of the pool. each gallon of finish will cover 200 square feet. how many gallons of paint will the hotel need to buy? select the correct answer. 7 gallons 10 gallons 9 gallons 8 gallons

Explanation:

Step1: Calculate rectangular - part area

Two side - walls: $2\times(50\times10)=1000$ square feet. One bottom - wall: $50\times10 = 500$ square feet. Two end - walls: $2\times(10\times10)=200$ square feet.

Step2: Calculate half - cylinder part area

Half - circular face: $\frac{1}{2}\times\pi\times6^{2}=18\pi\approx56.52$ square feet. Curved surface: $\frac{1}{2}\times2\pi\times6\times4 = 24\pi\approx75.36$ square feet.

Step3: Calculate total area

$1000 + 500+200+56.52 + 75.36=1831.88$ square feet.

Step4: Calculate number of gallons

$\frac{1831.88}{200}=9.1594\approx9$ gallons.

Answer:

9 gallons