The rectangular prism shown has a volume of 72 m3. This prism is enlarged using a scale factor of 3.
What is the volume of the enlarged prism?
The volume is prortional to the cube of its sides.
So the new volume is 3^3 or 27 times as large
To find the volume of the enlarged prism, we need to know the dimensions of the original prism. The volume of a rectangular prism is given by the formula:
Volume = length x width x height
Since we don't have the exact measurements of the original prism, we can use a general representation. Let's assume the dimensions of the original prism are represented as "l," "w," and "h".
So, the volume of the original prism is given by:
Volume_original = l x w x h
Now, let's consider the enlarged prism. We are told that it is enlarged using a scale factor of 3. This means that each dimension of the original prism is multiplied by 3 to get the corresponding dimension of the enlarged prism.
So, the dimensions of the enlarged prism are:
Length_enlarged = 3 x l
Width_enlarged = 3 x w
Height_enlarged = 3 x h
Therefore, the volume of the enlarged prism is given by:
Volume_enlarged = Length_enlarged x Width_enlarged x Height_enlarged
= (3 x l) x (3 x w) x (3 x h)
= 3^3 x l x w x h
= 27 x Volume_original
Given that the volume of the original prism is 72 m^3, we can substitute this value into the equation:
Volume_enlarged = 27 x Volume_original
= 27 x 72
= 1944 m^3
Hence, the volume of the enlarged prism is 1944 m^3.