Crazy cube

Calculus Level 2

If the area of any side of a cube is increasing at a rate of $2 \text{ m}^2/\text{s}$ , determine how fast its volume is increasing (in $\text{m}^{3}/\text{s}$ ) when the cube's side measures $6\text{ m}$ .

The answer is 18.

1 solution

Pulkit Gupta
Dec 10, 2015

Lets denote the area of any one of its sides by $a^{2}$ , then dA/dt = 2a da/dt . Hence da/dt = 1/ a { on putting dA/dt = 2 )

Now dV/dt = 3 $a^{2}$ da/dt . Evaluate.

Crazy cube

The answer is 18.

1 solution

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