Question Bank - Mathematics

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Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 2%

A.
0.12x2 (Decreasing)
B.
0.12x2 (Increasing)
C.
0.24x2 (Decreasing)
D.
0.24x2 (Increasing)

Solution:

Concept:Surface area of cube(S) = 6x2Calculation:Given: The surface area of a cube of side x meters And decreasing the side by 2%Now, the Surface area of the cube(S) = 6x2\( \Rightarrow \frac{{{\rm{dS}}}}{{{\rm{dx}}}} = \rm 12x\)According to question side decreasing by 2%= 2% of x= - 0.02x?x = - 0.002xThen approximation c change of surface area = ?S = ds = \(\rm({dS\over {dx}})? dx\)= 12x?(- 0.02x) = - 0.24x2 (Decreasing)

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