MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

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 thatThe 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 thatThe 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 diametersubstitute 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 gallonsremember that[tex]1\ ft^{3}=7.5\ gal[/tex]so[tex]95.68\ ft^{3}=95.68*7.5=718\ gal[/tex]