# Solid geometry help!!!

• Apr 26th 2007, 06:27 AM
Flower90
Solid geometry help!!!
Hi!!
You have a cube whose sides measure 1 cm and you section it with a plan which passes in the vertexs A, B,C
(look at the attachment). I need to find out the volume of the piramyd it originates from sectioning the cube.
http://www.artofproblemsolving.com/F...ops/spacer.gif
• Apr 26th 2007, 07:57 AM
Soroban
Hello, Flower90!

Quote:

You have a cube whose sides measure 1 cm and you section it
with a plane which passes in the vertexs A, B,C (see attachment).
Find the volume of the pyramid formed by sectioning the cube.

The pyramid has 4 faces: 3 isosceles right triangles and 1 equilateral triangle.

Set the pyramid on a table with one the right triangles on the bottom.

The volume of a pyramid is: .V .= .(1/3) × (area of base) × (height)

. . The base is a right triangle with sides 1 and 1; its area is: .½(1)(1) = 1/2

. . The height of the pyramid is 1.

Therefore, the volume is: .V .= .(1/3)(1/2)(1) .= .1/6

• Apr 26th 2007, 08:34 AM
Flower90
Thanks!!!!!!!!!!!:D :D :D