## Related questions with answers

Question

For the following exercise,

The volume $V$ of a sphere with respect to its radius $r$ is given by $V=\frac{4}{3} \pi r^3$.

Find the instantaneous rate of change of V when r = 3 cm.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 7To solve the given exercise we will use the definition of instantaneous rate of change and derivative which says: The instantaneous rate of change or derivative of a function $f(r)$ is given by formula

$\begin{aligned}\color{#c34632}{\boxed{f'(r)\color{#c34632}=\lim_{h\to0}\dfrac{f(r+h)-f(r)}{h}}}\tag{1}\end{aligned}$

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