Question
Download Solution PDFFind the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 2%
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Let the side of the cube is x meters,
Surface area of cube = S = 6 × (side)2
Approximate change in the surface area of the cube is given by:
Calculation:
Given: Side of the cube = x metres
Decrease in the side of cube = Δx = -2% of x (Negative sign indicate decreasing the quantity)
⇒ Δx = -0.02x
Now, Surface area of a cube is given by,
S = 6 × (side)2 = 6x2
Differentiating with respect to x, we get
⇒
Now,
The approximate change in the surface area of a cube =
Hence, the approximate change in the surface area of a cube is 0.24x2 metres2
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