Question

Ratios of Surface Area & Volume. Someone help. I'm confused on how to set it up.

Answer 1

the volume scale factor is
\[16:2\]
find the linear scale factor by finding cube root
\[(\sqrt[3]{16}:(\sqrt[3]{2})\]
now find the area scale factor by squaring
\[(\sqrt[3]{16})^{2}:(\sqrt[3]{2})^{2}\]
to get
\[16^{\frac{ 2 }{3 }}:2^{\frac{ 2 }{3 }}\]
\[\frac{ 16\frac{ 2 }{ 3 } }{ 2^{\frac{ 2 }{ 3 }} }=\frac{ 52 }{ x }\]
cross multiply and simplify to get x=13

Answer 2

hope you understood