An architect has created a scale drawing for a residential townhouse in the shape of a rectangular prism. In the drawing, the internal width of the townhouse is labeled as feet , the internal length as , and the internal height as . The local building department tells the architect that if built, the building would be too tall according to local zoning laws and that its height must be reduced by . If the architect creates a second scale drawing where the townhouse's height is reduced by , what will be its new proposed internal volume in cubic feet?

Question

An architect has created a scale drawing for a residential townhouse in the shape of a rectangular prism. In the drawing, the internal width of the townhouse is labeled as     feet    , the internal length as    , and the internal height as    . The local building department tells the architect that if built, the building would be too tall according to local zoning laws and that its height must be reduced by    . If the architect creates a second scale drawing where the townhouse's height is reduced by    , what will be its new proposed internal volume in cubic feet?

Bytelearn · Accepted Answer

Identify Dimensions: Identify the original dimensions of the townhouse. Width = w feet Length = l feet Height = h feetIdentify Height Reduction:  Step 2: Identify the height reduction. Height reduction = r feetCalculate New Height:  Step 3: Calculate the new height. New height = h - rCalculate New Volume:  Step 4: Calculate the new volume. Volume = Width * Length * New height Volume = w * l * (h - r)Check for Errors:  Step 5: Check for math errors. No errors found.

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