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Advanced Math/Amount Needed Follow-up


QUESTION: A wall is to be coated with stucco.


Length- 24'
Width- 12'
Height- 10'
Thickness- .5'

Calculate amount (square feet) of stucco needed to cover outside, inside, and top of wall.

I have included an illustration.


ANSWER: inside dimensions: length = 23 ft, width = 11 ft, height = 9.5 ft

inside area = 2(23×9.5) + 2(11×9.5) = 646 ft²

top area = 24×12 - 23×11 = 35 ft²

outside area = 2(24×10) + 2(12×10) = 720 ft²

stucco area = 899 + 35 + 720 = 1401 ft²

Be sure to check my numbers!

---------- FOLLOW-UP ----------

QUESTION: Some questions:

Is the inside area smaller because of the thickness?

Why is it subtracted in the top area?

How did you obtain the 899?

Thanks again.

Yes, the inside area is smaller because of the thickness of the walls.
899 was a mistake; sorry. I corrected it to 646 in one equation but not the other.

I think I made another error. My calculations were based on the assumption that there is a floor, the same thickness as the walls.
Now I think the floor should be treated as nonexistent or of negligible thickness. That makes the inside height the same as the outside height, so
   inside area = 2(23×10) + 2(11×10) = 680 ft²
   stucco area = 680 + 35 + 720 = 1435 ft²

The illustration indicates that there is no ceiling, so the top area is the area of a 24×12 rectangle, minus the area of the empty space.  

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Janet Yang


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