Answer:
Part a) [tex]V=1,000\ ft^{3}[/tex]
Part b) [tex]h=5\ ft[/tex]
Part c) [tex]=718\ gal[/tex]
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
[tex]V=LWH[/tex]
substitute the values
[tex]V=(25)(8)(5)=1,000\ ft^{3}[/tex]
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
[tex]V=\pi r^{2} h[/tex]
we have
[tex]V=1,000\ ft^{3}[/tex]
[tex]r=16/2=8\ ft[/tex] ----> the radius is half the diameter
substitute and solve for h
[tex]1,000=\pi (8)^{2} h[/tex]
[tex]h=1,000/(64 \pi)[/tex]
[tex]h=1,000/(64*3.14)=5\ ft[/tex]
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
[tex]1\ ft=12\ in[/tex]
so
[tex]6\ in=6/12=0.5\ ft[/tex]
Find the volume of water for [tex]h=5-0.5=4.5\ ft[/tex]
[tex]V=(3.14)(8)^{2}(4.5)=904.32\ ft^{3}[/tex]
so
the volume of water evaporated is equal to
[tex]1,000\ ft^{3}-904.32\ ft^{3}=95.68\ ft^{3}[/tex]
convert to gallons
remember that
[tex]1\ ft^{3}=7.5\ gal[/tex]
so
[tex]95.68\ ft^{3}=95.68*7.5=718\ gal[/tex]
