Question

Maria has a jewelry box and wants to increase its size. She finds one with four times the length, width, and height. How many times bigger will the volume of the new box be?

Answer 1

To get the scale factor of how much bigger the new box be, we let the dimensions of the smaller box equal to 1, and then get the volume.

`\begin{gathered} \text{Smaller box Volume} \\ l=1 \\ w=1 \\ h=1 \\ V_{\text{small box}}=l* w* h \\ V_{\text{small box}}=1*1*1 \\ V_{\text{small box}}=1\text{ cubic units} \end{gathered}`

Then we multiply all the dimensions with four, and get the volume, then divide it by the volume of the smaller box.

`\begin{gathered} \text{Bigger box} \\ l=1*4=4 \\ w=1*4=4 \\ h=1*4=4 \\ V_{\text{big box}}=4*4*4 \\ V_{\text{big box}}=64\text{ cubic units} \\ \\ \text{Divide it by the original box} \\ 64/1=64 \end{gathered}`

Therefore, the volume of the new box will be 64 times bigger.