Answer: 16: 49
Step-by-step explanation:
If two shapes are similar , then the following condition holds
(i) the ratio of their sides are equal
(ii) If [tex]l_{1}[/tex] is the length of the first one and [tex]l_{2}[/tex] is the length of the second one then:
[tex]\frac{A_{1} }{A_{2} }[/tex] = [tex]\frac{(L_{1} )^{2} }{L_{2}) ^{2} }[/tex]
Where A stands for the area
(iii) [tex]\frac{V_{1} }{V_{2} }[/tex] = [tex]\frac{(L_{1} )^{3} }{L_{2}) ^{3} }[/tex]
Following theses conditions , the ratio of the lengths of their edges is given to be 4 : 7 , then the ratio of their surface area implies:
[tex]\frac{A_{1} }{A_{2} }[/tex] = [tex]\frac{4^{2} }{7^{2} }[/tex]
[tex]\frac{A_{1} }{A_{2} }[/tex] = 16/49
Therefore the ratio of their surface area is 16: 49
