The length of the edge of the cube is 3.23 cm .
Step-by-step explanation:
We have , The relationship between the weight y gram and the edge x cm for a cube of gold is y = 19.3x3 or [tex]y = 19.3x^3[/tex] . A cube of gold weighs 652 grams i.e. y = 652 . Let's calculate value of x from above data:
[tex]y = 19.3x^3[/tex]
⇒ [tex]y = 19.3x^3[/tex]
⇒ [tex]652= 19.3x^3[/tex]
⇒ [tex]19.3x^3=652[/tex]
⇒ [tex]\frac{19.3}{19.3}x^3=\frac{652}{19.3}[/tex]
⇒ [tex]x^3=\frac{652}{19.3}[/tex]
⇒ [tex]\sqrt[\frac{1}{3} ]{x^3} = \sqrt[\frac{1}{3} ]{\frac{652}{19.3}}[/tex]
⇒ [tex]({x^3})^\frac{1}{3} =({\frac{652}{19.3}})^\frac{1}{3}[/tex]
⇒ [tex]x =(33.78)^\frac{1}{3}[/tex]
⇒ [tex]x =3.23[/tex]
Therefore, the length of the edge of the cube is 3.23cm.
