Question

Challenge A jewelry box has the shape of a rectangular prism. Find the volume of the jewelry box. If the height is increased by 3 in., by how much does the volume increase?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of the jewelry box, you need to multiply the length, width, and height of the box. Let's assume the original dimensions of the box are:

Length = L
Width = W
Height = H

So, the volume of the jewelry box is given by:
Volume = Length * Width * Height = L * W * H

If the height is increased by 3 inches, the new height would be H + 3. So the new volume would be:
New Volume = Length * Width * (Height + 3) = L * W * (H + 3)

To find by how much the volume increases, we can find the difference between the new volume and the original volume:
Increase in Volume = New Volume - Original Volume = L * W * (H + 3) - L * W * H

We can simplify this by factoring out L * W:
Increase in Volume = L * W * (H + 3 - H) = L * W * 3

Therefore, the volume increases by 3 times the original base area of the jewelry box.