Respuesta :
Answer:it is 3 to 4
Step-by-step explanation:
This is correct
The ratio of the edge lengths of the two cubes is 7 : 9.
What is surface area of cube?
The surface area of the cube can be defined as the total area covered by all six faces of the cube.
Given
The surface areas of two cubes have a ratio of 49 to 81.
Formula of surface area of cube = 6[tex]a^{2}[/tex]
Surface area of cube 1 = [tex]6a^{2} _{1}[/tex]
Surface area of cube 1 = [tex]6a^{2} _{2}[/tex]
Surface areas of two cubes have a ratio of 49 to 81.
[tex]\frac{6a^{2} _{1} }{6a^{2} _{2}}=\frac{49}{81}[/tex]
⇒ [tex]\frac{a^{2} _{1} }{a^{2} _{2}}=\frac{49}{81}[/tex]
⇒ [tex](\frac{a_{1} }{a_{2} } )^{2} =\frac{49}{81}[/tex]
⇒ [tex]\frac{a_{1} }{a_{2} } =\sqrt{\frac{49}{81} }[/tex]
⇒ [tex]\frac{a_{1} }{a_{2} } =\frac{7}{9} }[/tex]
⇒ [tex]a_{1}:a_{2} = 7:9[/tex]
Hence, the ratio of the edge lengths of the two cubes is 7 : 9.
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