The two square pyramids are similar. Find the total volume of both pyramids if the ratio of their surface areas is 9/16. Height of smaller pyramid is 6 in., and length of pyramid is 12 in.

Question

mathstudent55 · Answer

The ratio of the surface areas is the square of the ratio of the linear dimensions (length, height, width, etc.)
The ratio of the volumes is the cube of the ratio of the linear dimensions.

anonymous · Answer

I squared and had 3/4, now what do i do with that fraction with 6 and 12?

mathstudent55 · Answer

Good.
Since the ratio of their surface areas is 9/16, and that is the square of the ratios of the heights, then when you take the square root of 9/16 and get 3/4, you now have the ratio of their heights.
The ratio of their volumes is the cube of the ratio of the heights.
Ratio of volumes = (3/4)^3

mathstudent55 · Answer

Now you need to find their volumes.
The smaller pyramid has length 12 m and height 6 m.
You need to use the formula for the volume of a pyramid to find the volume.

$V_{pyramid} = \dfrac{1}{3}Bh$

where B = area of the base
and h = height of the pyramid

Since your pyramid is a square pyramid, the base is a square, and we are told the length of the side of the square is 12 m.
Find the area of the base, multiply by the height, and divide by 3.
That will give you the volume of the smaller pyramid.

Then use the ratio of the volumes we found above to find the volume of the larger pyramid.