Mathematics: Use function notation to represent how much the volume of the box (in cubic inches) changes by if the cutout length increases from 0.3 inches to 1.2 inches.

Use function notation to represent how much the volume

Squara

04.01.2022

Increases 64 times

Step-by-step explanation:

The volume of the box can be calculated using formula

$V=l\cdot w\cdot h,$

where

V = volume,

l = length,

w = width,

h = height

If the length was 0.3 inches, then the volume was

$V_1=0.3\cdot w\cdot h=0.3wh$

When the length became 1.2 inches, then all dimensions became 1.2 :0.3 =4 times greater, then the volume was

$V_2=1.2\cdot (4w)\cdot (4h)=19.2wh$

The volume increases

$\dfrac{V_2}{V_1}=\dfrac{1.92wh}{0.3wh}=64$ times

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