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

Answer:

Lateral areas have ratio of 4:1

Volumes have ratio of 8:1

Step-by-step 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 $\frac{5\frac{1}{2} }{2\frac{3}{4} }$ which if you simplify it, it is $\frac{5.5}{2.75}$, 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 $8:1$