Calculate volume using double integrals

[leslie8167]

What is the volume of a barn that has a rectangular base 20 ft by 40 ft, vertical walls 30 ft high at the front (which we assume is on the 20-ft side of the barn), and 40 ft high at the rear? The barn has a flat roof. Use double integrals to compute the volume.

 

[HallsofIvy]

What is the volume of a barn that has a rectangular base 20 ft by 40 ft, vertical walls 30 ft high at the front (which we assume is on the 20-ft side of the barn), and 40 ft high at the rear? The barn has a flat roof. Use double integrals to compute the volume.

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You try, yourself, first. Show us what you have tried to do first and then we will help you.

 

[pootette]

I know this may slightly break the rules, but I will give you a hint: pretend the barn is a trapezoidal prism (an odd block, if you will). Put the floor/base along the plane that is created by the x and y-axis (the roof will extend in the z direction). This will *help* set up the double integrals...