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Application Of Derivatives

Question

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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 1%.

Solution

Let S be surface area of cube of side x metre.

therefore space space space space space space space straight S space equals space 6 straight x squared

Now,

dS space equals space open parentheses dS over dx close parentheses increment straight x space equals space 12 space straight x space increment straight x space space space space

equals 12 straight x left parenthesis negative 0.01 space straight x right parenthesis space space space space space space space space space space space space space space space space space space space open square brackets because space space 1 percent sign space of space straight x space is space 0.01 space straight x close square brackets equals space minus 0.12 space straight x squared

therefore space space space space approximate space change space in space volume space equals space 0.12 space straight x squared space straight m squared left parenthesis numerically right parenthesis.

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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