An 18-wheel truck driver had his fuel gauge break while making a delivery. He di
ID: 2882608 • Letter: A
Question
An 18-wheel truck driver had his fuel gauge break while making a delivery. He didn’t have time to have it repaired, so he decided to use a long stick to dip into the fuel tank and measure how much fuel remained.
The circular section of the tank had a radius of 2 feet, and the driver knew that the tank would hold 200.0 gallons of fuel when it was totally fuel.
1. Find the length of the tank, show how you did this.
2. When the driver dipped the stick down into the tank to check the fuel, the stick was wet with fuel, 3.0 feet up the stick. He reasoned correctly that the tank was half full, plus another 1 foot of depth. Does this mean that the tank is ¾ full? Explain.
3. Determine the amount of fuel in the tank when the stick showed 3.0 feet of depth for the fuel, by using this method:
a. Make a sketch of the tank in the xyz coordinate system. Position it so one circular end is on the yz plane, where the center of the circle is at the origin. (0,0,0)
b. Find the equation for the top of the tank (in form z=f(x,y)).
c. Find the equation of a plane which is parallel to the xy-plane, and represents the surface of the fuel.
d. Use a double (or triple) integral to find the volume of the fuel remaining in the tank.
4. There are other ways to determine the volume of fuel in the tank. Try another method to see if the answer from part c. is correct.
I hope someone can answer all of the parts. Thank you in advance!
Explanation / Answer
given,
radius of tank = 2 feet.
we know that ,
volume of tank = pi x R 2 x l
=> 200 gallons = 3.14 * 2*2*l cubic feet
=>26.7361 = 12.56l
=> l = 2.12 feet.
therefore the lenght of tank is 2.12 feet.
here all tthe remainnig cases are not possible becoz it is mentioned that the stick is wet by 3 feet which cant be possible
hence found.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.