Question

Given the conversion factor which cube has the larger surface area?

Answer 1

Given the surface area of a cube as

$\begin{gathered} SA=6l^2 \\ \text{where l is the length} \end{gathered}$

Given Cubes A and B

$\begin{gathered} \text{Cube A} \\ l=19.5ft \end{gathered}$$\begin{gathered} \text{Cube B } \\ l=6m\text{ } \\ \text{ in ft}\Rightarrow\text{ 1m =3.28ft} \\ l=6\times3.28ft=19.68ft \end{gathered}$

Find the surface area of the cubes and compare them to know which one is larger

$\begin{gathered} \text{Cube A} \\ SA=6\times19.5^2=6\times380.25=2281.5ft^2 \end{gathered}$$\begin{gathered} \text{Cube B} \\ SA=6\times19.68^2=6\times387.3024=2323.8144ft^2 \end{gathered}$

Hence, from the surface area gotten above, Cube B has a larger surface area than Cube A