Vito has an 8-inch by 10-inch piece of cardstock. He cuts it in the shape shown below and folds it on the dotted lines. He tapes the sides to make the box shown below. What is the surface area of the box?
Is it:
48 sq in.
24 sq in.
52 sq in.
60 sq in.
To find the surface area of the box, we need to calculate the area of each individual face and then add them up.
First, let's find the area of the base of the box. The base is a rectangle with dimensions 8 inches by 10 inches, so its area is 8 inches * 10 inches = 80 square inches.
Next, let's find the area of the four sides of the box. Each side is a rectangle with a width of 8 inches and a height of 6 inches (10 inches - 2 inches cut off by folding and taping). So the area of each side is 8 inches * 6 inches = 48 square inches.
There are four sides, so the total area of the four sides is 4 sides * 48 square inches/side = 192 square inches.
Finally, we add the area of the base and the area of the four sides to find the total surface area of the box: 80 square inches + 192 square inches = 272 square inches.
Therefore, the correct answer is not one of the options given. The surface area of the box is 272 sq in.
To find the surface area of the box, we need to calculate the area of each face and then add them together.
The box consists of four rectangular faces and two square faces.
Step 1: Calculate the area of the rectangular faces:
Two opposite faces have dimensions 8 inches by 10 inches.
Area of each rectangular face = length × width = 8 inches × 10 inches = 80 square inches
Step 2: Calculate the area of the other two rectangular faces:
Two opposite faces have dimensions 8 inches by x inches, where x is the height of the box.
Area of each rectangular face = length × width = 8 inches × x inches = 8x square inches
Step 3: Calculate the area of the two square faces:
The dimensions of each square face are x inches by x inches.
Area of each square face = side × side = x inches × x inches = x^2 square inches
Step 4: Calculate the total surface area of the box:
Total Surface Area = 2 × (Area of rectangular faces) + 2 × (Area of square faces)
= 2 × (80 square inches) + 2 × (x^2 square inches)
= 160 square inches + 2x^2 square inches
Based on the given information, we don't have the value of x, so we can't determine the exact surface area. Therefore, it seems there is a mistake in the provided options.
To find the surface area of the box, we need to calculate the area of each of its six faces and then add them together.
First, let's identify the dimensions of each face of the box:
1. The base of the box has dimensions 8 inches by 10 inches.
2. The two sides have dimensions 8 inches by the height of the cutout shape (let's call it h).
3. The other two sides have dimensions 10 inches by h.
Now, let's calculate the area of each face:
1. The area of the base is length × width = 8 in × 10 in = 80 sq in.
2. The area of each of the two identical side faces is 8 in × h.
3. The area of each of the other two identical side faces is 10 in × h.
Since there are two side faces with dimensions 8 in × h and two side faces with dimensions 10 in × h, we can calculate:
Area of the four side faces = 2 × (8 in × h) + 2 × (10 in × h) = 16h + 20h = 36h sq in.
Finally, we add up the areas of all six faces:
Total surface area = area of the base + area of the four side faces
Total surface area = 80 sq in + 36h sq in
To determine the answer, we need the value of h, which is not given in the question. Could you provide the height of the cutout shape (h)?