Question

The edge of a cube is decreasing at the rate of 0.04 cm/sec. If the edge of the cube is 10 ems, then rate of decrease of surface area of the cube is ______.

Options

• 4.8 cm²/sec

• 4.08 cm²/sec

• 48 cm²/sec

• 4.008 cm²/sec

Answer 1

The edge of a cube is decreasing at the rate of 0.04 cm/sec. If the edge of the cube is 10 ems, then rate of decrease of surface area of the cube is 4.8 cm²/sec.

Explanation:

Let edge of a cube be x cm, then surface area of the cube, A = 6x²

It is given that, `"dx"/"dt"` = - 0.04 cm/sec

Now, `"dA"/"dt" = 12 x "dx"/"dt"`

= 12x(- 0.04)

= - 0.48 x

when, x = 10, then `"dA"/"dt" = - 0.48 xx 10 = - 4.8 "cm"^2//"sec"`