A rectangular prism has dimension of length 8cm, height 9cm and width 6cm.
The prism expanded at a constant rate until the width was 8cm. If the other dimension also expanded at the same constant rate, find the volume of the rectangular prism after its expansion.
the width has grown by a factor of 4/3
so, the volume has grown by a factor of (4/3)^3
a rectangular has dimensions of 6cm,9cm and 12cm
To find the volume of the rectangular prism after its expansion, we need to determine the new dimensions of the prism.
We know that initially, the width of the prism was 6cm and it expanded until it reached 8cm. This means that the width increased by 2cm. Since the width increased at a constant rate, we can assume that the other dimensions also increased by 2cm.
So, after the expansion, the new dimensions of the rectangular prism would be:
Length = 8cm + 2cm = 10cm
Height = 9cm + 2cm = 11cm
Width = 8cm
Now, we can calculate the volume of the expanded prism by multiplying its length, height, and width together:
Volume = Length x Height x Width
Volume = 10cm x 11cm x 8cm
Volume = 880cm³
Therefore, the volume of the rectangular prism after its expansion is 880 cubic centimeters.