Question

Your friend's swimming pool is in the shape of a rectangular prism, with a length of 25 feet, a width of 8 feet, and a height of 5 feet. a. What is the volume of your friend's swimming pool? b. Your swimming pool is in the shape of a cylinder with a diameter of 16 feet and has the same volume as your friend's pool. What is the height of your pool? Round your answer to the nearest whole number. c. While you were on vacation, 6 inches of water evaporated from your pool. About how many gallons of water evaporated from your pool? ( ) 3 1 ft 7.5 gal ? Round your answer to the nearest whole number.

Answer 1

a. The volume of the rectangular prism is 1000 cubic feet. b. The height of the cylindrical pool is 4 feet. c. About 750 gallons of water evaporated from the pool.

Step-by-step explanation:

a. The volume of the rectangular prism can be found by multiplying the length, width, and height. So, the volume is 25 * 8 * 5 = 1000 cubic feet.

b. Since the two pools have the same volume, we can use the formula for the volume of a cylinder (V = πr²h) to find the height of the cylinder. We know the diameter is 16 feet, so the radius is half of that, which is 8 feet. Plugging it into the formula, 1000 = 3.142 * 8² * h. Solving for h, we find h = 4 feet.

c. To find the gallons of water evaporated, we need to convert the units. 6 inches is 0.5 feet. The volume evaporated is 25 * 8 * 0.5 = 100 cubic feet. Since 1 cubic foot is equal to 7.5 gallons, the amount evaporated is 100 * 7.5 = 750 gallons.

Answer 2

Part a)
`V=1,000\ ft^(3)`

Part b)
`h=5\ ft`

Part c)
`=718\ gal`

Step-by-step explanation:

Part a) What is the volume of your friend's swimming pool?

we know that

The volume of a rectangular prism is equal to

`V=LWH`

substitute the values

`V=(25)(8)(5)=1,000\ ft^(3)`

Part b) Your swimming pool is in the shape of a cylinder with a diameter of 16 feet and has the same volume as your friend's pool. What is the height of your pool?

we know that

The volume of a cylinder is equal to

`V=\pi r^(2) h`

we have

`V=1,000\ ft^(3)`

`r=16/2=8\ ft` ----> the radius is half the diameter

substitute and solve for h

`1,000=\pi (8)^(2) h`

`h=1,000/(64 \pi)`

`h=1,000/(64*3.14)=5\ ft`

Part c) While you were on vacation, 6 inches of water evaporated from your pool. About how many gallons of water evaporated from your pool?

remember that

`1\ ft=12\ in`

so

`6\ in=6/12=0.5\ ft`

Find the volume of water for
`h=5-0.5=4.5\ ft`

`V=(3.14)(8)^(2)(4.5)=904.32\ ft^(3)`

so

the volume of water evaporated is equal to

`1,000\ ft^(3)-904.32\ ft^(3)=95.68\ ft^(3)`

convert to gallons

remember that

`1\ ft^(3)=7.5\ gal`

so

`95.68\ ft^(3)=95.68*7.5=718\ gal`