Question

I need help with this questionSmall cube 8.3) medium cube 16.7) large cube 25.0

Answer 1

For the small box

we have the dimension to be 8.3

The surface area can be calculated as follow

`\begin{gathered} \text{Surface Area(SA)=6}* L* L \\ =6*8.3*8.3 \\ =413.34 \end{gathered}`

The volume of the small cube is

`\begin{gathered} \text{Volume}=L* L* L \\ \text{Volume}=8.3*8.3*8.3 \\ \text{Volume}=571.787 \end{gathered}`

The ratio of the surface area to the volume is given as

`\begin{gathered} (SA)/(V)=(413.34)/(571.787) \\ (SA)/(V)=0.723 \end{gathered}`

For the medium cube

Length = 16.7

The surface area will be

`\begin{gathered} SA=6*16.7*16.7 \\ SA=1673.34 \end{gathered}`

The volume will be

`\begin{gathered} \text{Volume}=16.7*16.7*16.7 \\ \text{Volume}=4657.463 \end{gathered}`

The ratio of the surface area to the volume will be

`(SA)/(V)=(1673.34)/(4657.463)=0.359`

For the Large cube

The length is given as: 25.0

The surface area of the cube will be

`\begin{gathered} SA=6*25*25 \\ SA=3750 \end{gathered}`

The volume of the cube will be

`\begin{gathered} \text{Volume}=25*25*25 \\ \text{Volume}=15625 \end{gathered}`

The ratio of the surface area to the volume will be

`\begin{gathered} (SA)/(V)=(3750)/(15625) \\ (SA)/(V)=0.24 \end{gathered}`