ABCDEFGH shown below is a cube with volume 1. Find the volume of pyramid ABCH.
volume of pyramid = (1/3)(area of base)(height)
Let right triangle ABC be the pyramid base and HD be the height.
Let's find the edge length of the cube.
volume of cube = (edge length)3
1 = (edge length)3
1 = edge length
Let's find the area of right triangle ABC .
area of triangle ABC = (1/2)(AB)(BC)
area of triangle ABC = (1/2)(1)(1)
area of triangle ABC = 1/2
HD is an edge of the cube so
HD = 1
volume of pyramid = (1/3)(area of triangle ABC)(HD)
volume of pyramid = (1/3)(1/2)(1)
volume of pyramid = 1/6 cubic units
volume of pyramid = (1/3)(area of base)(height)
Let right triangle ABC be the pyramid base and HD be the height.
Let's find the edge length of the cube.
volume of cube = (edge length)3
1 = (edge length)3
1 = edge length
Let's find the area of right triangle ABC .
area of triangle ABC = (1/2)(AB)(BC)
area of triangle ABC = (1/2)(1)(1)
area of triangle ABC = 1/2
HD is an edge of the cube so
HD = 1
volume of pyramid = (1/3)(area of triangle ABC)(HD)
volume of pyramid = (1/3)(1/2)(1)
volume of pyramid = 1/6 cubic units