Question

If the edge of a cube increases at the rate of$60cm$ per second, at what rate the volume is increasing when the edge is $90cm$

• A. $48600cucmpersec$
• B. $1458000cucmpersec$
• C. $4374000cucmpersec$
• D. None of the above

Answer 1

The correct option is B

$1458000cucmpersec$

Explanation for correct option

Given the edge of a cube increases at the rate of$60cm$ per second and length of the edge is $90cm$

Let $a$ be the length of each side of the cube i.e. $a$ $=90cm$

Then the volume of the cube is $V=a^3$

Now rate in change in volume

$$\begin{gathered} \Rightarrow \frac{dV}{dt}=\frac{d\left(a^3\right)}{dt} \\ \Rightarrow \frac{dV}{dt}=3a^2\frac{da}{dt} \\ \Rightarrow \frac{dV}{dt}=3·{\left(90\right)}^2·60 \\ \Rightarrow \frac{dV}{dt}=145800c{m}^3/sec \end{gathered}$$

Hence option (B) is correct i.e. $1458000cucmpersec$