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A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2 cm/s.

(a) Express the radius $ r $ of the balloon as a function of the time $ t $ (in seconds).(b) If $ V $ is the volume of the balloon as a function of the radius, find $ V \circ r $ and interpret it.

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a) $r(t)=2 t $b) $V \circ r=\frac{32}{3} \pi t^{3} $

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 3

New Functions from Old Functions

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

David Base G.

October 26, 2020

That was not easy, glad this was able to help

Kinley M.

February 2, 2021

A balloon in the shape of a sphere is being inflated at the rate of 2 cm/sec. At the time at which the radius of the balloon is 3cm, how fast is its radius increasing?

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Lectures

04:31

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

0:00

A spherical balloon is bei…

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01:05

02:04

$$\begin{array}{l}{\te…

01:58

The radius $r,$ in inches,…

02:59

The radius $r$ , in inches…

05:32

00:58

01:19

Suppose a spherical balloo…

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