Calculate the volumes of the original and increased prism and then compare.
The volume is increased by a factor of 8.
Practice makes perfect
Let's calculate the volume of the original prism and the volume of the prism with the doubled dimensions, and then compare them.
Volume of the Original Prism
In order to calculate the volume of the prism we can use the determined formula.
V=wl h
Here w is the width, l is the length, and h is the height of the prism. We are given that the rectangular prism has a width of 18 cm, a length of 12 cm, and a height of 22 cm. By substituting these values into the formula we can calculate the prism's volume.
After the dimensions of the original prism are doubled, we get the following new dimensions.
{ lw=18cm l=12cm h=22cm ⇒ { lw=18* 2= 36cm l=12* 2= 24cm h=22* 2= 44cm
Let's again substitute these values into the volume formula and calculate V_(increased).
Let's now compare the found volumes of the original and increased prism.
V_(original)=4752 cm^3
V_(increased)=38 016 cm^3
To find how much the volume of the increased prism is greater that the volume of the original prism, we can divide the second value by the first one.
