Respuesta :
The volume of recangular prism can be calculated as:
[tex]V=w\cdot l\cdot h[/tex]V: volume
w: width
l: length
h: height
The box heigth has been increased by 15%, this means that to the original heigth 0.15% of it has been added:
Let "x" represent the original height of the box
[tex]\begin{gathered} h=x+0.15x \\ h=1.15x \end{gathered}[/tex]The box length has been increased by 25%, this means that to the original length, 0.25 more has been added
Let "y" represent the length of the box:
[tex]\begin{gathered} l=y+0.25y \\ l=1.25y \end{gathered}[/tex]Let "z" represent the original width of the box.
The original volume of the box can be calculated as:
[tex]V_{\text{old}}=xyz[/tex]And the new volume of the box can be calculated as
[tex]V_{\text{new}}=1.15x\cdot1.25y\cdot z[/tex]To calculate the percentage increase you have to subtract the old volume from the new one and divide it by the old volume.
[tex]\begin{gathered} \text{Increase}=\frac{V_{\text{new}}-V_{\text{old}}}{V_{\text{old}}}_{} \\ \text{Increase}=\frac{(1.15x\cdot1.25y\cdot z)-(xyz)}{xyz} \\ \text{Increase=}\frac{2.4xyz-xyx}{xyz} \\ \text{Increase}=\frac{1.4xyz}{zyx} \\ \text{Increase}=1.4 \end{gathered}[/tex]The 1 represents the original volume, so that the box volume was increased 0.4 of its original volume.
Multiply it by 100 and the percentaje is 40%
