A box in the shape of a rectangular prism has a volume of 56 cubic

inches. If the length of each side is multiplied by 2, what will be the
approximate volume of the resulting box?

V = 2^3(56) = 448 cubic in.

wrong!!!

To find the approximate volume of the resulting box after multiplying the length of each side by 2, we need to understand how volume is affected by scaling.

The volume of a rectangular prism is calculated by multiplying the length, width, and height together. In this case, we know that the original volume of the box is 56 cubic inches.

Let's denote the original length, width, and height of the box as l, w, and h respectively. Since it is a rectangular prism, all three sides are different.

So, the original volume, V1, can be expressed as V1 = l * w * h.

Now, we are multiplying the length of each side by 2. Let's call the new length, width, and height of the resulting box as L, W, and H respectively.

To find the new volume, V2, we calculate V2 = L * W * H.

Since each side is multiplied by 2, we have L = 2l, W = 2w, and H = 2h.

Substituting these values into V2, we get V2 = (2l) * (2w) * (2h) = 8 * l * w * h.

Therefore, the approximate volume of the resulting box is approximately 8 times the volume of the original box.

To find the approximate volume, we multiply the original volume by 8:
V2 ≈ 8 * V1

Substituting the original volume V1 = 56 cubic inches, we get:
V2 ≈ 8 * 56 = 448 cubic inches

So, the approximate volume of the resulting box is 448 cubic inches.