Question

The edge of a cube is decreasing at the rate of 0.6 cm/sec. Find the rate at which its volume is decreasing when the edge of the cube is 2 cm. ​

Answer 1

Explanation:

Solution

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Let x be the edge of the cube and V be its volume at any time t.

Then V=x

3

Differentiating w.r.t t we get

dt

dA

=3x

2

dt

dx

Now,

dt

dx

=

sec

0.6 cm

and x=2 cm

∴

dt

dV

=3(2)

2

(0.6)

+7.2

Hence, the volume of the cube is decreasing at the rate of

sec

7.2 cm