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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. What volume of materials was used to make all the columns in the palace?

A
100,000 m3
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B
110,000 m3
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C
120,000 m3
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D
130,000 m3
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Solution

The correct option is C 120,000 m3
In a Triangular prism shaped column, base is a triangle stretched to a certain height.



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 = 600m3×200
Total Volume = 120,000 m3

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