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Nataly [62]
2 years ago
5

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:

Mathematics
1 answer:
N76 [4]2 years ago
5 0

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

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