Question

`the side of a cube decreases at the rate of 0.04 cm/sec .the rate of decrease in the volume of the cube when the side is 10cm`​

Answer 1

Answer:

apply volume formula

volume of the cube=a3

decreased side =0.04

so the side is=a-0.04a

=a(1-0.04)

=(0.96)a

volume of the cube=a0.96^3

decreased percent of volume is=0.884a^3

Answer 2

Answer:

Volume of the cube decrease at the rate of $12cm^{3}/sec$

Step-by-step explanation:

Explanation:

Given , Side of a cube decreases at rate = 0.04cm/sec

⇒$\frac{da}{dt} = 0.04 cm /sec$

Let the side of the cube be 'a'

So the volume of the cube = $a^{3}$

⇒ V = $a^{3}$

Differentiating  both side w.r.t ''t''.

⇒$\frac{dV}{dt} = 3a^{2} \frac{da}{dt}$

⇒$\frac{dV}{dt} = 3a^{2} (0.04)$

But we have side of cube = 10cm

⇒$\frac{dV}{dt} = 3(10)^{2} (0.04)$

⇒$\frac{dV}{dt} = 12cm^{3}/sec$

Final answer :

Hence , Volume of the cube decrease at the rate of $12cm^{3}/sec$

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