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The length, the breadth and the height of a closed cuboidal box are 2.5 m, 2 m and 90 cm, respectively. What would be the cost of a canvas needed to cover this box completely, if the cost of the canvas is ₹70 per m2?
₹1,507
₹1,267
₹1,448
₹1,348
₹1,267
Convert all dimensions to meters first (90 cm=0.9 m), calculate total surface area of the cuboid, then multiply by the cost per square meter.
Length l=2.5 m, breadth b=2 m, height h=90 cm=0.9 m, rate of canvas = ₹70 per m2
C=2(lb+bh+hl)×Rate
Convert all dimensions to meters first (90 cm=0.9 m), calculate total surface area of the cuboid, then multiply by the cost per square meter.
Forgetting to convert centimeters into meters for the height or missing one of the six faces of the closed box.
Step 1: Convert all units to meters
The length and breadth are already in meters, but the height is given in centimeters. Convert height to meters: h=90 cm=10090 m=0.9 m.
h=0.9 m
Step 2: Find the Total Surface Area of the Cuboid
Since the box is closed, use the total surface area formula for a cuboid: TSA=2(lb+bh+hl).
TSA=2(2.5×2+2×0.9+0.9×2.5)
Step 3: Evaluate TSA
Calculate each product inside the parentheses: 2.5×2=5, 2×0.9=1.8, and 0.9×2.5=2.25. Sum them up: 5+1.8+2.25=9.05. Multiply by 2: TSA=2×9.05=18.1 m2.
TSA=18.1 m2
Step 4: Calculate the Total Cost of the Canvas
Multiply the total surface area by the cost per square meter: Cost=18.1×70=1267 ₹.
Cost=₹1,267
B is correct because the total surface area of the cuboid is 18.1 m2 and multiplying it by the rate of ₹70 per m2 yields ₹1,267.
Always ensure all dimensions share consistent units before applying mensuration formulas to avoid severe calculation errors.