SOLUTION: A trophy is made of a glass triangular prism attached to a 0.5 inch high wooden block shaped like a square prism. The height of the triangular prism is 6 inches. The volume of the
Algebra ->
Pythagorean-theorem
-> SOLUTION: A trophy is made of a glass triangular prism attached to a 0.5 inch high wooden block shaped like a square prism. The height of the triangular prism is 6 inches. The volume of the
Log On
Question 1134583: A trophy is made of a glass triangular prism attached to a 0.5 inch high wooden block shaped like a square prism. The height of the triangular prism is 6 inches. The volume of the wooden base is 4.5 cubic inches. Find the volume of the entire trophy, including the base. Answer by Theo(13342) (Show Source):
you are given that the height of the square baser is .5 inches and that the volume of the square prism that forms the block is 4.5 cubic inches.
if you let x equal the length of each side of the square, then the volume of the block will be .5 * x^2 = 4.5 cubic inches.
solve for x^2 to get x^2 = 4.5 / .5 = 9.
this makes x = 3.
that's the length of each side of the top face of the square block.
the triangular prism is going to sit on the top face of the square block.
the height of each trianglular face of the prism will be 6 inches.
the area of each triangular face of the prism will be 1/2 * 3 * 6 = 9.
the volume of the triangular prism will be 9 * 3 = 27 cubic inches.
the total volume will be 4.5 + 27 = 31.5 cubic inches.
here's my picture of what i think the trophy will look like.
