Question

select the correct answer from each drop - down menu. complete the statements about these similar pyramids. pyramid a. pyramid b. the ratio of the heights is. the ratio of the base areas is. the ratio of the volumes is.

Explanation:

Step1: Find the ratio of the heights

The height of Pyramid A is 15 m and the height of Pyramid B is 5 m. The ratio of the heights of Pyramid A to Pyramid B is $\frac{15}{5}=3:1$.

Step2: Recall the relationship for base - area ratio of similar solids

For two similar solids, if the ratio of their corresponding linear dimensions (such as heights) is $a:b$, the ratio of their base - areas is $a^{2}:b^{2}$. Since the ratio of the heights is $3:1$, the ratio of the base - areas is $3^{2}:1^{2}=9:1$.

Step3: Recall the relationship for volume ratio of similar solids

For two similar solids, if the ratio of their corresponding linear dimensions (such as heights) is $a:b$, the ratio of their volumes is $a^{3}:b^{3}$. Since the ratio of the heights is $3:1$, the ratio of the volumes is $3^{3}:1^{3}=27:1$.

Answer:

The ratio of the heights is 3:1.
The ratio of the base - areas is 9:1.
The ratio of the volumes is 27:1.