If the dimensions of the rectangular prism are increased 4 times, the surface area will increase 8 times.
no, it will grow by a factor of 4^2 = 16
nope... lol i dont know
To understand why the surface area of a rectangular prism increases by a factor of 8 when its dimensions are increased by a factor of 4, let's break it down and analyze the formula for surface area.
The surface area (SA) of a rectangular prism can be calculated using the formula:
SA = 2lw + 2lh + 2wh
where l, w, and h represent the length, width, and height of the prism, respectively.
Let's assume we have a rectangular prism with the original dimensions l, w, and h. If each dimension is increased by a factor of 4, the new dimensions of the prism will be 4l, 4w, and 4h.
Substituting these new dimensions into the surface area formula, we get:
SA_new = 2(4l)(4w) + 2(4l)(4h) + 2(4w)(4h)
= 8lw + 8lh + 8wh
We can see that the surface area of the enlarged prism is 8 times the original surface area (SA_new = 8SA) since each term in the equation is multiplied by 8.
Therefore, when the dimensions of a rectangular prism are increased by a factor of 4, the surface area will increase by a factor of 8.