Question

The ratio of the corresponding edge lengths of two similar solids is 2:5. What is the ratio of their surface areas?

Answer 1

The ratio of the surface areas of two similar solids with edge length ratio 2:5 is 4:25, as the surface area ratio is the square of the edge length ratio.

Step-by-step explanation:

The ratio of the corresponding edge lengths of two similar solids is 2:5. The ratio of their surface areas will be the square of the ratio of their edge lengths, because surface area is a two-dimensional measure (length squared).

Therefore, to find the ratio of their surface areas, you square the ratio of their edge lengths:

• Edge length ratio: 2:5
• Surface area ratio: (22):(52)
• Surface area ratio: 4:25

So the ratio of the surface areas of the two similar solids is 4:25.

Answer 2

4: 25

l1=2
l2=5

surface area= 6*l^2

so for 1st =6*2^2
2nd= 6*5^2

ratio=6*2^2 /6*5^2

ratio= 4/25
or 4:25