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A day full of math games & activities. Find one near you.
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 = x3
Now,
dV/dt = d/dt (x3)
= d/dx (x3) dx/dt
On differentiating wrt t we get,
= 3x2 dx/dt
We have,
dx/dt = 3 cm/s
Hence,
dV/dt = 3x2 (3)
= 9x2
So, when x = 10 cm
Then,
dV/dt = 9 (10)2
= 900 cm3/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 cm3/s
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