The edge of a cube is decreasingg at the rate of 0.04 cm/sec. if the edge of the cube is 10 cms, then rate of decrease of surface area of the cube is . . .

Options

A. `4.8cm^(2)//sec`
B. `4.08cm^(2)//sec`
C. `48cm^(2)//sec`
D. `4.008cm^(2)//sec`

Answer

A

Explanation

Let edge of a cube be x cm, then surface area of the cube, `A=6x^(2)`
it is given that, `(dx)/(dt)=-0.04cm//sec`
Now, `(dA)/(dt)=12x(dx)/(dt)=12x(-0.04)=-0.48x`
when, x=10, then `(dA)/(dt)=-0.48xx10=-4.8cm^(2)//sec`