It takes 1/8 of a roll of wrapping paper to completely cover all 6 sides of a small box that is shaped like a rectangular prism. The box has a volume of 10 cubic inches. Suppose the dimensions of the box are tripled (k=3).
To find the new volume of the box after the dimensions are tripled, we can use the formula for the volume of a rectangular prism, which is V = l * w * h, where "l," "w," and "h" are the length, width, and height of the prism.
In this case, the original volume of the box is 10 cubic inches. Let's call the original dimensions of the box as l1, w1, and h1, and the new dimensions as l2, w2, and h2.
We know that k = 3, which means each side length is multiplied by 3 when the dimensions are tripled. So, we can write the equation:
l2 = k * l1
w2 = k * w1
h2 = k * h1
Substituting the values:
l2 = 3 * l1
w2 = 3 * w1
h2 = 3 * h1
The new volume, V2, is given by:
V2 = l2 * w2 * h2
Plugging in the values:
V2 = (3 * l1) * (3 * w1) * (3 * h1)
V2 = 27 * (l1 * w1 * h1)
Since the original volume is 10, we have:
27 * (l1 * w1 * h1) = 10
Dividing both sides by 27:
l1 * w1 * h1 = 10 / 27
Therefore, the new volume V2 is 10/27 cubic inches.