Two boxes must be wrapped. Both boxes are right rectangular prisms. The smaller box has a length of 12 inches. The larger box is similar to the first and has a length of 48 inches. Find the ratio of the amount of paper needed to wrap the large box to the amount of paper needed to wrap the small box.

I'm thinkin that since the larger box is 4 times the smaller, then it would be 4 x 4 x 4 = 64:1, but that just doesn't sound right.

Any help would be greatly appreciated!!

wouldn't it be just 4:1 because 48/12=4. 12 is 1/4 of 48 hence.. 4:1

To find the ratio of the amount of paper needed to wrap the large box to the amount of paper needed to wrap the small box, you need to consider the surface area of each box.

The surface area of a right rectangular prism can be found by adding up the areas of all six faces.

Let's start with the smaller box:

The dimensions of the smaller box are not provided, other than the length of 12 inches. So we'll assume it is a cube, which means all sides have the same length.

If the length of the smaller box is 12 inches, then all sides of the smaller box would also be 12 inches.

The surface area of the smaller box is then given by:

Surface area of smaller box = 6 * (Side length)^2

Surface area of smaller box = 6 * (12 inches)^2

Surface area of smaller box = 6 * 144 square inches

Surface area of smaller box = 864 square inches

Now let's move on to the larger box:

The larger box is similar to the smaller box, which means their corresponding sides are proportional. In this case, the length of the larger box is 48 inches, which is 4 times the length of the smaller box.

Since the length is 4 times larger, all other sides will also be 4 times larger.

The surface area of the larger box is then given by:

Surface area of larger box = 6 * (Side length)^2

Surface area of larger box = 6 * (48 inches)^2

Surface area of larger box = 6 * 2304 square inches

Surface area of larger box = 13824 square inches

Finally, to find the ratio of the amount of paper needed, divide the surface area of the larger box by the surface area of the smaller box:

Ratio = Surface area of larger box / Surface area of smaller box

Ratio = 13824 square inches / 864 square inches

Ratio ≈ 16:1

So, the ratio of the amount of paper needed to wrap the large box to the amount of paper needed to wrap the small box is approximately 16:1.