Answer:
Step-by-step explanation:
Volumes of two spheres A and B = 648 cm³ and 1029 cm³
Things to remember:
1). Scale factor of two objects = [tex]\frac{r_1}{r_2}[/tex] [[tex]r_1[/tex] and [tex]r_2[/tex] are the radii of two circles]
2). Area scale factor = [tex]\frac{(r_1)^2}{(r_2)^2}[/tex]
3). Volume scale factor = [tex]\frac{(r_1)^3}{(r_2)^3}[/tex]
Volume scale factor Or Volume ratio = [tex]\frac{V_A}{V_B}[/tex]
[tex]\frac{(r_1)^3}{(r_2)^3}= \frac{648}{1029}[/tex]
[tex]\frac{r_1}{r_2}=\sqrt[3]{\frac{648}{1029} }[/tex]
[tex]\frac{r_1}{r_2}=\frac{6(\sqrt[3]{3})}{7(\sqrt[3]{3})}[/tex]
[tex]\frac{r_1}{r_2}=\frac{6}{7}[/tex]
Therefore, scale factor = [tex]\frac{r_1}{r_2}=\frac{6}{7}[/tex]
≈ 6 : 7
Area scale factor Or area ratio = [tex](\frac{r_1}{r_2})^2=(\frac{6}{7})^2[/tex]
= [tex]\frac{36}{49}[/tex]
≈ 36 : 49
Volume scale factor or Volume ratio = [tex]\frac{648}{1029}[/tex]
= [tex]\frac{216}{343}[/tex]
≈ 216 : 343
