An open box has external breadth 12 cm, length 15 cm and height 10 cm. If the thickness of the material of the box is 1 cm, calculate the total surface area of the box. (Hint; there are 14 surfaces).
The external dimensions of the box are 15 cm by 12 cm by 10 cm.
If the thickness of the material is 1 cm, then the internal dimensions of the box are (15 - 2) cm by (12 - 2) cm by (10 - 2) cm.
The surface area of the bottom of the box is 15 cm * 12 cm = 180 cm^2.
The surface area of the top of the box is also 180 cm^2.
The surface area of the front of the box is (15 - 2) cm * (10 - 2) cm = 104 cm^2.
The surface area of the back of the box is also 104 cm^2.
The surface area of the left side of the box is (12 - 2) cm * (10 - 2) cm = 80 cm^2.
The surface area of the right side of the box is also 80 cm^2.
The total surface area of the box is 2 * (180 cm^2) + 2 * (104 cm^2) + 2 * (80 cm^2) = 628 cm^2. Answer: \boxed{628}.
To calculate the total surface area of the box, we need to find the area of each surface and then sum them up.
The box has 6 faces: top, bottom, front, back, left side, and right side. Each of these faces has a thickness of 1 cm, so we need to subtract 1 cm from each dimension to find the internal dimensions of the box.
The internal dimensions would be:
- Internal breadth = 12 cm - 2 cm (thickness) = 10 cm
- Internal length = 15 cm - 2 cm (thickness) = 13 cm
- Internal height = 10 cm - 2 cm (thickness) = 8 cm
Now, let's calculate the area of each surface:
1. Top and bottom surfaces: Each has the same dimensions, so we calculate the area of one and double it.
- Area = 10 cm * 13 cm = 130 cm²
- Total area = 2 * 130 cm² = 260 cm²
2. Front and back surfaces: Each has the same dimensions, so we calculate the area of one and double it.
- Area = 10 cm * 8 cm = 80 cm²
- Total area = 2 * 80 cm² = 160 cm²
3. Left and right side surfaces: Each has the same dimensions, so we calculate the area of one and double it.
- Area = 13 cm * 8 cm = 104 cm²
- Total area = 2 * 104 cm² = 208 cm²
Now, let's calculate the area of the internal faces (the faces that were subtracted because of the thickness):
4. Internal top and bottom surfaces: Same as the external top and bottom surfaces.
- Total area = 2 * 130 cm² = 260 cm²
5. Internal front and back surfaces: Same as the external front and back surfaces.
- Total area = 2 * 80 cm² = 160 cm²
6. Internal left and right side surfaces: Same as the external left and right side surfaces.
- Total area = 2 * 104 cm² = 208 cm²
Now, let's sum up all the surface areas:
Total surface area = 260 cm² (external top/bottom) + 160 cm² (external front/back) + 208 cm² (external left/right)
+ 260 cm² (internal top/bottom) + 160 cm² (internal front/back) + 208 cm² (internal left/right)
Total surface area = 1056 cm²
Therefore, the total surface area of the box is 1056 cm².