two similar solids have corresponding lengths in the ratio 2:5. Determine the ratio of the lateral area
(2/5)^2
as I explained in the other problem
So it would be 4/25?
So the next questiona asks to determine the ratio of the volumes so would I do (2/5)^3 and get .064 or 8/125?
atsa right
To determine the ratio of the lateral area of two similar solids, you need to understand the concept of similarity and how it relates to the ratio of their corresponding sides.
When two solids are similar, it means that their corresponding sides are in proportion or ratio. In this case, the corresponding lengths of the two solids are in the ratio of 2:5.
Let's say the first solid has a length measured as 2x, and the second solid has a length measured as 5x. Here, x represents a common multiplier that scales up the lengths in proportion.
Now, the lateral area of a solid refers to the area of all its faces except the top and bottom faces (i.e., the base). Since the two solids are similar, their lateral areas will also be proportional.
To find the ratio of the lateral areas, we need to compare the areas of their corresponding faces. Since the ratio of their lengths is 2:5, the ratio of their corresponding areas will be the square of that ratio, which is (2:5)^2 or (2/5)^2.
Therefore, the ratio of the lateral area of the two similar solids will be:
(2/5)^2 = 4/25
So, the ratio of the lateral area is 4:25.