From a 10-inch-by-19-inch piece of cardboard, 3-inch-square corners are cut out, as shown in the figure above, and the resulting flaps are folded up to form an open box.
Find the surface area and volume of the open box
With 3 inches cut from each corner, the dimensions would be (10-6) by (19-6).
V = 4 * 13 * 3 = ?
If it is the surface area within the box, in other words, the bottom, 4 * 13 = ?
To find the surface area and volume of the open box, we need to follow a few steps:
Step 1: Determine the dimensions of the box.
The original piece of cardboard measures 10 inches by 19 inches. By cutting out 3-inch squares from each corner, the resulting box will have a length, width, and height.
The length of the box = 19 inches - 2 * 3 inches = 13 inches
The width of the box = 10 inches - 2 * 3 inches = 4 inches
The height of the box = 3 inches
Step 2: Calculate the surface area of the open box.
The surface area of the box is the sum of the areas of all six sides. In this case, the box has three rectangular sides and three flaps.
Rectangular sides:
1. Length * Width = 13 inches * 4 inches = 52 square inches
2. Length * Height = 13 inches * 3 inches = 39 square inches
3. Width * Height = 4 inches * 3 inches = 12 square inches
Flaps:
1. Length * Height = 13 inches * 3 inches = 39 square inches
2. Width * Height = 4 inches * 3 inches = 12 square inches
3. Width * Height = 4 inches * 3 inches = 12 square inches
Total surface area = 52 + 39 + 12 + 39 + 12 + 12 = 166 square inches
Step 3: Calculate the volume of the open box.
The volume of a rectangular prism is calculated by multiplying the length, width, and height.
Volume = Length * Width * Height = 13 inches * 4 inches * 3 inches = 156 cubic inches
Therefore, the surface area of the open box is 166 square inches, and the volume of the open box is 156 cubic inches.