CONCEPTUAL PhUSICS PRACTICE PAGE

Chapter $12$ Solids

Scaling

Consider a cube, say $1cm1cm1cm($a very small sugar cube$),$ Its volume is $1c{m}^3.$ The surface area of one of its faces is $1c{m}^2.$ The total surface area of the cube is $6c{m}^2,$ because it has six sides. Now consider a second cube, scaled up by a factor of $2$ so it is $2cm2cm2cm.$

a$.$ What is the total surface area of each cube?

$1^{st}$ cube $c{m}^2$;$2^{nd}$ cube $24q,c{m}^2$

b$.$ What are the volumes of each cube?

$1^{st}$ cube $c{m}^3$;$2^{nd}$ cube $m^3$

c$.$ Compare the surface$-$area$-$to$-$volume ratio for

$1^{st}$ cube of $\frac{\text{s}\text{u}\text{r}\text{f}\text{a}\text{c}\text{e}\text{a}\text{r}\text{e}\text{a}}{\text{v}\text{o}\text{l}\text{u}\text{m}\text{e}}=,$;$2^{nd}$ cube of $\frac{\text{s}\text{u}\text{r}\text{f}\text{a}\text{c}\text{e}\text{a}\text{r}\text{e}\text{a}}{\text{v}\text{o}\text{l}\text{u}\text{m}\text{e}}=$