Answer:
volume of the rectangular prism will increase by a factor of 64.
Explanation:
The surface area of a rectangular prism is increase by a factor of 16.
We know surface area is calculated by multiplication of 2 dimensions.
A ∝ length²
√A ∝ length
Therefore, increase in length of the sides will be = √16 = 4
Now we know volume is a unit in which 3 dimensions are multiplied ( length × width × height )
If Increase in length of sides is 4 times then volume will increase by 4³
V ∝ length³
V ∝ (4 × length)³ = 64 × (length)³
Therefore, volume of the rectangular prism will increase by a factor of 64.