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Question

# The columns in the ancient palace were made up of triangular prisms that were 50 m tall. The base is a triangle with a side of 8 m and the perpendicular down to the 8 m side is 3 m. There were 200 such columns. If the cost of the material is 2/m3 . The total cost of materials needed to build all 200 columns would be

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Solution

## In a Triangular prism-shaped column, the base is a triangle stretched to a certain height. Cost of material = 2 dollars/ m3 Total cost of material needed = Total volume of material × Cost of material Total cost of material = Total volume of 200 columns × 2 dollars/ m3 Here, Length of one of the side of triangular base = 8 m Length of perpendicular to one of the side = 3 m Volume of material used in the hall = Volume of 1 column × Number of columns Column is prism shaped, therefore Volume of material =200× Volume of 1 prism Area of triangular base = Area of base × height =12×8×3 = 12 m2 Volume of Triangular prism = Area of triangle × height = 12 m2× height Height = 50 m = 12 m2× 50 m Volume of 1 triangular prism = 600 m3 Number of Prisms = 200 Total Volume = 600 m3×200 = 120,000 m3 ∴ Total Cost of all Prisms = 120,000 m3× 2/m3 = \$240,000 240,000 dollars is the total cost of material needed.

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