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Find the cost (in ₹) of digging a cuboidal pit 9 m long, 5 m broad and 4 m deep at the rate of ₹20 per m³.
3,900
3,800
3,700
3,600
3,600
Calculate volume as 9×5×4=180. Since rate is 20, simply double the volume (180×2=360) and add a zero: 3600.
Length (l) = 9 m, Breadth (b) = 5 m, Depth/Height (h) = 4 m, Rate of digging = ₹20 per m³.
Cost=Volume×Rate where Volume=l×b×h
Calculate volume as 9×5×4=180. Since rate is 20, simply double the volume (180×2=360) and add a zero: 3600.
Confusing surface area with volume; remember that digging a pit involves excavation of the entire internal capacity (volume), not just surface area.
Calculate Volume
The volume of a cuboid is found using the formula V=l×b×h. Substituting the given dimensions: 9×5×4=180.
V=9×5×4=180 m3
Calculate Total Cost
Total cost is the product of the volume and the rate per cubic meter: Cost=180×20.
Cost=180×20=3600
D is correct because the total volume of 180 m³ multiplied by the rate of ₹20/m³ results in ₹3,600.
This concept of 'Volume × Rate' is identical to the 'Area × Rate' principle used in flooring or painting problems; always identify if the task requires capacity (volume) or surface coverage (area).
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