Answer:
Part 1) The volume of pyramid A is two times the volume of pyramid B
Part 2) The new volume of pyramid B is equal to the volume of pyramid A
Step-by-step explanation:
we know that
The volume of a pyramid is equal to
where
B is the area of the base of pyramid
h is the height of the pyramid
Part 1
<em>The heights of the pyramids are the same</em>
<em> Find the volume of pyramid A</em>
Find the area of the base B
substitute
<em>Find the volume of pyramid B</em>
Find the area of the base B
substitute
Compare the volumes
The volume of pyramid A is two times the volume of pyramid B
Part 2)
If the height of pyramid B increases to twice that of pyramid A
we have that
<em>Find the new volume of pyramid B</em>
we have
substitute
Compare the volumes
The new volume of pyramid B is equal to the volume of pyramid A