Question

Pyramid A has height 5 1/2, and Pyramid B has height 2 3/4. A and B are similar. What is the ratio of their:

Lateral areas?
Volumes?

Answer 1

Lateral areas have ratio of 4:1

Volumes have ratio of 8:1

Explanation:

There is a rule in 3D geometry that when two solids are similar, and their edges are in the ratio of
`a:b`, the ratio of any surface area type measure is always
`a^2:b^2` this includes the lateral area, which is just a surface area minus the base, which is not important for this problem. The ratio of volumes of those similar solids is in the ratio of
`a^3:b^3\\`.

Now, to solve this, we need to find the ratio of any corresponding length of these similar pyramids. We have both the heights, so if we form a ratio of
`(5(1)/(2) )/(2(3)/(4) )` which if you simplify it, it is
`(5.5)/(2.75)`, which is
`2`. The ratio of the heights are
`2:1`.

Now we can apply those rules to this ratio, the ratio of lateral areas would then be
`2^2:1^2`, which is
`4:1`. the ratio of volumes would be
`2^3:1^3`, which is
`8:1`