Geometry Problem: surface area of a 30inch square by 10ft duct.

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Mac81

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It's been awhile since I used basic formulas but I can't figure this question out. What is the surface area of a 30inch square by 10ft duct. The answer is 105ft2 but I cant figure out how they got it. The duct is a rectangle.
 
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First, convert every measurement to feet.
Second, show your best efforts, please.
Third, Are you sure we have all the necessary information?
 
Yes that is all the info. I got the answer once put can't replicate it. It has been awhile. Its a rectangular prism
 
I'm assuming the ends of the duct are open (i.e., no surface covering either end).

A rectangular prism has length, width, and height.

The duct is 10 feet long, 30 inches wide, and 30 inches high.

Therefore, the total surface is the sum of four identical areas -- each one belonging to a rectangle measuring 10 feet by 30 inches.

The area for a rectangle is the product of its two dimensions (measured in identical units, of course).

Area = Length × Width

or

Area = Length × Height

Something seems wrong with your information because I don't get 105 square feet.
 
Mac81 said:
Yes that is all the info. I got the answer once put can't replicate it. It has been awhile. Its a rectangular prism
Click to expand...

Well, then, whoever gave you this problem to solve is a bit of a jerk, as it is literally impossible to solve. The formula for the surface area of a rectangular prism is A = 2(wl + wh + hl), where w is the width, l is the length, h is the height, and A is the surface area. Since we're solving concerned with finding the surface area, the dimensions are interchangeable, so let's just say that the given dimensions are a length of 30 inches and a width of 10 feet. We'll also note that 30 inches = 2.5 feet. Accordingly the formula now is:

A = 2(10 * 2.5 + 10 * h + h * 2.5)

As you can see, without knowing the height, it is impossible to proceed further. Given the answer from the answer key, we can of course work backwards to determine what the height must be, but otherwise the problem is very poorly formulated. I'd strongly consider having a chat with whoever gave you this problem.
 
Oh! That does make a lot of sense. It still doesn't result in the given answer, so something's hinky with this problem.
 
Mac81 said:
I got 2*(w+h)*L+2*(w*h) = 112.5 ft^2
Click to expand...
With algebraic expressions, we don't use the letter x to show multiplication; we use an asterisk. Also, upper- and lower-case symbols are not interchangeable.

112.5 ft^2 is correct for the outer surface area of the duct, if each end is capped (i.e., no openings anywhere).

If the duct's ends are open, then the outer surface area is 100 ft^2. :cool:
 
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