Calculate the total surface area of the cuboid of dimensions 6m by 5m by 7.5m
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The total surface area of a cuboid is given by the formula:
SA = 2lw + 2lh + 2wh
Where:
l = length
w = width
h = height
Substituting the given values:
SA = 2(6 x 5) + 2(6 x 7.5) + 2(5 x 7.5)
SA = 60 + 90 + 75
SA = 225
Therefore, the total surface area of the given cuboid is 225 m².
To calculate the total surface area of a cuboid, you need to find the areas of all six faces and then add them together.
Step 1: Find the area of the first face (base) by multiplying the length (6m) by the width (5m):
Area of the base = length * width = 6m * 5m = 30m^2
Step 2: Find the area of the second face (top) by multiplying the length (6m) by the width (5m):
Area of the top = length * width = 6m * 5m = 30m^2
Step 3: Find the area of the third face (front) by multiplying the height (7.5m) by the width (5m):
Area of the front = height * width = 7.5m * 5m = 37.5m^2
Step 4: Find the area of the fourth face (back) by multiplying the height (7.5m) by the width (5m):
Area of the back = height * width = 7.5m * 5m = 37.5m^2
Step 5: Find the area of the fifth face (left side) by multiplying the length (6m) by the height (7.5m):
Area of the left side = length * height = 6m * 7.5m = 45m^2
Step 6: Find the area of the sixth face (right side) by multiplying the length (6m) by the height (7.5m):
Area of the right side = length * height = 6m * 7.5m = 45m^2
Step 7: Add up the areas of all six faces to find the total surface area:
Total surface area = Area of the base + Area of the top + Area of the front + Area of the back + Area of the left side + Area of the right side
Total surface area = 30m^2 + 30m^2 + 37.5m^2 + 37.5m^2 + 45m^2 + 45m^2
Total surface area = 225m^2 + 75m^2 + 90m^2
Total surface area = 390m^2
Therefore, the total surface area of the cuboid is 390 square meters.