Question

The solid triangular prism shown below is made from metal . The prism is melted down and the metal is used to create a solid cube. Find the side length of the cube. The height of the prism is 12. The base is 9. There is a line going down the middle which is 4. Also the side length of the prism is 6.

Answer 1

The side length of the cube is : 6.868 units

Explanation:

The volume of a triangular prism is given as;

v= base area * length

v=1/2 b*h*l where b is the base length, h is the height of the prism and l is the side length of the prism

Given that : b=9, h=12,l=6

v= 1/2 * 9*12*6 =324 cubic units

Volume of a cube is given as;

v=l³ where l is side length of the cube

324= l³

`\sqrt[3]{324} =l\\\\6.868=l`