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 m${}^3$
• B. 110,000 m${}^3$
• C. 120,000 m${}^3$
• D. 130,000 m${}^3$

Answer 1

The correct option is C 120,000 m${}^3$

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 $\times$ Number of columns

Column is prism shaped, therefore
Volume of material =$200\times$ Volume of 1 prism

Area of triangular base = Area of base $\times$ height
$=\frac{1}{2}\times 8\times 3$
= 12 m${}^2$

Volume of Triangular prism = Area of triangle $\times$ height
= 12 m${}^2\times$ height
Height = 50 m
= 12 m${}^2\times$ 50 m
Volume of 1 triangular prism = 600 m${}^3$



Number of Prisms = 200
Total Volume = 600m${}^3\times 200$
$\therefore$ Total Volume = 120,000 m${}^3$