An open box whose shape is a cubiod has dimension 9cm by 7cm by 6cm find the outer surface area of the box and it volume
The outer surface area of the box can be found by adding up the areas of all six faces.
Area of one face = length x width
Face 1: 9cm x 7cm = 63cm²
Face 2: 9cm x 6cm = 54cm²
Face 3: 7cm x 6cm = 42cm²
Total area of these three faces = 63cm² + 54cm² + 42cm² = 159cm²
Since there are two of each type of face (front/back, top/bottom, left/right), the total surface area is:
2(63cm²) + 2(54cm²) + 2(42cm²) = 2(159cm²) = 318cm²
The volume of the box can be found by multiplying length x width x height:
Volume = 9cm x 7cm x 6cm = 378cm³
To find the outer surface area of the box, we need to find the total area of all six sides.
Step 1: Find the area of each face
The box has three pairs of faces that have the same dimensions:
- The front and back faces have dimensions 9cm by 7cm (area = 9cm * 7cm = 63cm²)
- The top and bottom faces have dimensions 9cm by 6cm (area = 9cm * 6cm = 54cm²)
- The left and right faces have dimensions 7cm by 6cm (area = 7cm * 6cm = 42cm²)
Step 2: Calculate the total surface area
Now, add up the areas of all six faces:
63cm² (front) + 63cm² (back) + 54cm² (top) + 54cm² (bottom) + 42cm² (left) + 42cm² (right) = 318cm²
Therefore, the outer surface area of the box is 318cm².
To find the volume of the box, simply multiply the dimensions together:
Volume = length * width * height
Volume = 9cm * 7cm * 6cm
Volume = 378cm³
Therefore, the volume of the box is 378cm³.