SOLUTION: Good day, can you help me with this problem? An inverted square pyramid has a height equal to 24 cm. It holds water to a depth of 18 cm above its apex. Find the volume of it

Algebra ->  Bodies-in-space -> SOLUTION: Good day, can you help me with this problem? An inverted square pyramid has a height equal to 24 cm. It holds water to a depth of 18 cm above its apex. Find the volume of it      Log On


   

Question 1005909: Good day, can you help me with this problem?

An inverted square pyramid has a height equal to 24 cm. It holds water to a depth of 18 cm above its apex. Find the volume of its content if the top face has an area of 100 cm^2.
Thank you!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There is a square base pyramid with
a base area of 100cm%5E2 , and
a height of 24cm .
The volume of a pyramid with base area B and height h is
V%5Bpyr%5D=Bh%2F3 .
So the volume of the pyramid is
V%5Bpyr%5D=%28100cm%5E2%29%2A%2824cm%29%2F3=800cm%5E3 .
That pyramid is inverted and filled with water to a height/depth of 18cm .
So, you have a pyramid of water inside the original pyramid.
Both pyramids are similar solids, meaning that the water pyramid is a scaled-down version of the original pyramid.
The scale is 18%3A24 ,
meaning that every length measurement in the water pyramid is
18%2F24=3%2F4 of the corresponding measurement in the original pyramid.
The ratio of volumes of similar solids is the cube of the ratio of corresponding length measurements.
So the volume of water in this problem is
.