The Volume of an Auxiliary Fuel Tank for a Helicopter?

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SUMMARY

The discussion focuses on calculating the volume of an auxiliary fuel tank designed for a helicopter, generated by revolving the function y = 1 - (x^2/16) around the x-axis, within the bounds of -4 to 4 feet. The initial integral setup was 2*pi∫(0 to 4) (1 - (x^2/16)) dx, which led to an incorrect volume calculation of 17 cubic feet. The correct volume is essential for determining the additional flight range, as the tank's capacity directly influences the helicopter's fuel efficiency and distance capabilities.

PREREQUISITES
  • Understanding of integral calculus, specifically volume of revolution
  • Familiarity with the concept of cubic feet and conversion to gallons
  • Basic knowledge of helicopter fuel consumption metrics
  • Experience with setting up and evaluating definite integrals
NEXT STEPS
  • Review the method for calculating volumes of solids of revolution using the disk method
  • Learn about the application of integrals in real-world engineering problems
  • Explore fuel efficiency calculations for aircraft, including conversions between volume and distance
  • Investigate common mistakes in integral calculus and how to avoid them
USEFUL FOR

Aerospace engineers, students studying calculus, and professionals involved in helicopter design and fuel efficiency optimization will benefit from this discussion.

acdougla17
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I think I did this right but I want to make sure since it is an extra credit problem and I could use the points. If I did something incorrect, I don't want an answer, just point me in the right direction so I can work it out myself.

You are designing an auxiliary fuel tank that will fit under a helicopters fuselage to extend its range. The shape of the tank is generated by revolving y = 1 - (x^2/16), -4<= x => 4 around the x-axis (dimensions in feet).

a) How many cubic feet of fuel will the tank hold (to the nearest cubic foot)?
I set up the integral as 2*pi∫(0 to 4) 1- (x^2/16) dx
My answer was 17 cubic feet

b)A cubic foot holds 7.481 gal. If the helicopter gets 2mi to the gallon, how many additional miles can it fly with the new tank?
My answer 254.354 miles
 
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Your answer to (b) is right given your answer to part (a), but you didn't calculate the volume correctly.
 

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