A prism and pyramid have congruent bases and the same length of altitude. If the volume of the pyramid is 24 in^3 , find the volume of the prism.

Question

Geometry Question

Answer 1

Prisms and pyramids behave similarly - their volume is dependent on the area of the base and their altitude. This is true for all prisms (including "circular prisms" or cylinders) and for all pyramids (including "circular pyramids" or cones).

 

The volume of any prism is the area of the base times the altitude of the prism.

 

The volume of a pyramid is 1/3 the area of the base times the altitude of the pyramid.

 

As a formula:

 

V_prism = Area_base x altitude

 

V_pyramid = 1/3 x Area_base x altitude

 

If the bases of the two solids are congruent, their areas are equal, and we know the altitudes are equal.

 

So the quantity ( Area_base x altitude ) is the same in both equations.

 

Substituting the volume of the prism into the formula for the volume of the pyramid:

 

V_pyramid = 1/3 x V_prism

 

At this point, you can solve for the volume of the prism easily since you know the volume of the pyramid.