A rectangular prism has a volume of 280cm cubed. If the scale factor of a second rectangular prism is 2.5, what is the volume of the second rectangular prism?

volume is proportional to the cube of their corresponding sides

V/280 = 2.5^3/1^3
V = 280(15.625)
= 4375 cm^3

To find the volume of the second rectangular prism, we need to understand how the volume of a three-dimensional object changes with a scale factor.

The volume of a rectangular prism is given by the formula V = l * w * h, where l is the length, w is the width, and h is the height.

Here, we are given that the volume of the first rectangular prism is 280 cm^3.

Let's assume the length, width, and height of the first rectangular prism are l1, w1, and h1, respectively.

So we can write the equation as:
V1 = l1 * w1 * h1 = 280 cm^3.

Now, we are given that the scale factor of the second rectangular prism is 2.5. This means the length, width, and height of the second rectangular prism will be 2.5 times larger than that of the first rectangular prism.

Let's denote the length, width, and height of the second rectangular prism as l2, w2, and h2, respectively.

Using the scale factor, we can write the relationship between the dimensions of the first and second rectangular prism as:
l2 = 2.5 * l1 (length is scaled by 2.5)
w2 = 2.5 * w1 (width is scaled by 2.5)
h2 = 2.5 * h1 (height is scaled by 2.5)

Now, to find the volume of the second rectangular prism, we can substitute the values of l2, w2, and h2 in the volume formula:

V2 = l2 * w2 * h2 = (2.5 * l1) * (2.5 * w1) * (2.5 * h1)
= 2.5 * 2.5 * 2.5 * (l1 * w1 * h1)
= 2.5^3 * V1

We already know that V1 = 280 cm^3, so we can substitute it into the formula:

V2 = 2.5^3 * V1 = 2.5^3 * 280 cm^3

Now, we can calculate the volume of the second rectangular prism by simplifying the expression:

V2 = 2.5^3 * 280 = 2.5 * 2.5 * 2.5 * 280 = 1562.5 cm^3

Therefore, the volume of the second rectangular prism is 1562.5 cm^3.