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/m${}^3$ . The total cost of materials needed to build all 200 columns would be

Answer 1

In a Triangular prism-shaped column, the base is a triangle stretched to a certain height.


Cost of material = 2 dollars/ m${}^3$
Total cost of material needed = Total volume of material $\times$ Cost of material
Total cost of material = Total volume of 200 columns $\times$ 2 dollars/ m${}^3$

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 $\times$ 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 = 600 m${}^3\times 200$
= 120,000 m${}^3$

$\therefore$ Total Cost of all Prisms = 120,000 m${}^3\times$ 2/m${}^3$
= $240,000
240,000 dollars is the total cost of material needed.