Video Transcript
Given that approximately 7.5
gallons of water can fill one cubic foot, roughly how many whole gallons of water
would be in a cylindrical water tank with diameter 20 feet and height 12 feet, if it
was full?
In this question, we are asked to
estimate the number of gallons of water that would fill a cylindrical water tank
with diameter 20 feet and height 12 feet to the nearest whole number of gallons. To estimate this value, let’s start
by sketching a picture of the cylindrical water tank. Remember, a cylinder is a shape
with two circular faces of the same side connected by a tube. We are told the diameter of the
circles is 20 feet and the height of the cylinder is 12 feet. Since we want to determine the
amount of water in the full tank, we need to find the volume of the tank.
We can recall that the volume of a
prism or cylinder is equal to the area of its base times its height. Since the faces are circles, the
area of the base is 𝜋𝑟 squared, where 𝑟 is the radius of the circle. We can find the radius of the
circular faces by halving the diameter. The radii are of length 10
feet. We can now find the volume of the
cylinder by substituting 𝑟 equals 10 feet and ℎ equals 12 feet into the equation to
get 𝑣 equals 𝜋 times 10 squared times 12. We can calculate that 10 squared
times 12 is 1,200, so the volume of the water tank is 1,200𝜋 cubic feet.
Remember though, we are tasked with
finding the number of gallons of water that fills the tank, not the number of cubic
feet of water that fills the tank. We are told in the question that
one cubic foot is approximately equal to 7.5 gallons. If we multiply both sides of this
estimation by 1,200𝜋, then we will find an estimate for the volume of the tank in
gallons, where it is worth noting that this is the same as multiplying the volume of
the cylinder in cubic feet by 7.5 to approximately convert the volume into
gallons. In either case, we find that the
volume of the water tank is approximately 1,200𝜋 times 7.5 gallons. Evaluating this expression using a
calculator gives us 28,274.3 and this expansion continues gallons.
Finally, we round this value to the
nearest whole number to see that approximately 28,274 gallons of water will fill the
water tank to the nearest whole number of gallons.
