Question

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A rectangular resort pool has a length of 45 feet and a width of 30 feet. A sitting area is attached to the pool and is in the shape of a semicircle with a diameter of 20 feet, as shown below. If the pool is filled to a depth of 5 feet and the sitting area is filled to a depth of 2.5 feet, approximately how much water is contained in both the sitting area and the pool?

Athletic Outfitters packs tennis balls into a cylinder with a diameter of 9.6 centimeters and a height of 39.5 centimeters. Each tennis ball has a diameter of 9.5 centimeters and there are 4tennis balls in each container. Approximately how much extra space is in the container?

Answer 1

1 7142.699082ft³ (C)

2 1063.420642cm³ (A)

Explanation:

Hey There!

1. So for the first one we want to find the volume of the rectangular pool and the volume of the semi cylinder

The dimension given are

length - 45

width - 30

height - 5

to find the volume we use

`V=lwh`

`45*30=1350\\1350x5=6750`

so the volume of the rectangular pool is 6750ft³

now we need to find the volume of the semi cylinder

the dimensions given are

diameter - 20

height - 2.5

so we find the volume by using the volume for a cylinder then dividing by 2

the volume for a cylinder formula is

`V=\pi r^2h`

r = radius

h = height

to find the radius given the diameter we just divide by 2

20/2=10 so the radius is 10

now we just plug in the values and get

`V=(1)/(2) \pi 10^22.5`

Note: the 1/2 is added because were finding the volume of a semi cylinder

`10^2=100\\100(2.5)=250\\250\pi =785.3981634\\(785.3981634)/(2) =392.6990817`

So the volume of the sitting area is 392.6990817

Now that we have found the volume of each part we add them together to get the answer

`392.6990817+6750=7142.699082`

2. For the second one we need to find the volume of the cylinder and subtract it by the volume of the tennis ball..s times 4 ( because there are 4 of them)

For the cylinder we are given the dimensions

height - 39.5

diameter - 9.5

Remember this is the formula of the volume of a cylinder

`V=\pi r^2h`

r =radius

h = height

to convert diameter to radius we divide by 2

9.5/2=4.75

now we plug in the values

`V=\pi 4.75^239.5\\4.75^2=22.5625\\22.565(39.5)=891.21875\\891.21875\pi =2859.100642`

so the volume of the container is 2859.100642cm³

now we need to find the volume of the tennis ball

to do this we use the formula

`V=(4)/(3) \pi r^3`

we are given the dimensions of

diameter - 9.5

once again to convert to radius we divide by 2

9.5/2=4.75

now we plug in the values

`V=(4)/(3) \pi 4.75^3\\4.75^3=107.171875\\107.171875(4)/(3) =142.8958333\\142.8958333\pi =448.9205002\\448.9205002(4)=1795.682001`

So the volume of the tennis bal...ls is 1795.682001

note: i multiplied by 4 because there are 4 tennis bal...ls

our final step is to subtract the volume of the bal...ls from the container

2859.100642-1795.682001=1063.420642

hope this helps :)