# An edge of a variable cube is increasing at the rate of 3cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

**Solution:**

In maths, derivatives have wide usage. They are used in many situations like finding maxima or minima of a function, finding the slope of the curve, and even inflection point

Let the length and the volume of the cube respectively be x and V.

Hence, V = x^{3}

Now,

dV/dt = d/dt (x^{3})

= d/dx (x^{3}) dx/dt

On differentiating wrt t we get,

= 3x^{2} dx/dt

We have,

dx/dt = 3 cm/s

Hence,

dV/dt = 3x^{2} (3)

= 9x^{2}

So, when x = 10 cm

Then,

dV/dt = 9 (10)^{2}

= 900 cm^{3}/s

NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.1 Question 4

## An edge of a variable cube is increasing at the rate of 3cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

**Summary:**

Given that edge of a variable cube is increasing at the rate of 3cm/s. Hence, the volume of the cube increasing when the edge is 10 cm long is 900 cm^{3}/s

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