Answer:
False.
Step-by-step explanation:
Let us consider two similar cuboids A and B as shown in the figure below.
We have that,
'A' has length, width and height 5, 3 and 4 units respectively.
'B' has length, width and height 7.5, 4.5 and 6 units respectively.
Also, surface area of a cuboid = 2 × ( L + W + H ), where L= length, W= width and H= height.
Now, we will find the surface area of A and B.
Surface area of A, [tex]S_{A}[/tex] = 2 × ( 5 + 3 + 4 ) = 2 × 12 = 24
Surface area of B, [tex]S_{B}[/tex] = 2 × ( 7.5 + 4.5 + 6 ) = 2 × 18 = 36
Therefore, the ratio of the surface area is [tex]S_{A}[/tex] : [tex]S_{B}[/tex] = 24 : 36 = 2 : 3.
Moreover, the ratio of square root of lengths is given by [tex]\sqrt{L_{A}} : \sqrt{L_{B}} = \sqrt{5} : \sqrt{7.5}[/tex] = 2.24 : 2.74
Hence, we see that the ratio of the surface area of two similar solids is not equal to the square root of the ratio between their corresponding edge lengths.
