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 ABCDEFGH shown below is a cube with volume 1. Find the volume of pyramid ABCH.

Confusedperson  Jun 21, 2018

Best Answer 

 #1
avatar+7336 
+1

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

hectictar  Jun 21, 2018
 #1
avatar+7336 
+1
Best Answer

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

hectictar  Jun 21, 2018

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