Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please solve RD Sharma class 12 chapter Derivative As a Rate Measure exercise 12.2 question 21 maths textbook solution

Please solve RD Sharma class 12 chapter Derivative As a Rate Measure exercise 12.2 question 21 maths textbook solution

Answers (1)

Answer: 6 \mathrm{~cm}^{3} / \mathrm{sec}

Hint: The surface area of the bubble will be, S A=4 \pi r^{2} .

Given: The surface area of a spherical bubble is increasing at the rate of 2 cm2/sec

Solution: To find rate of increase of its volume, when the radius is 6 cm.

Let the radius of the given spherical bubble be r cm at any instant time.

It is given that the surface area of a spherical bubble is increasing at the rate of 2 \mathrm{~cm}^{2} / \sec \frac{d s}{d t}=2

\begin{aligned} &S=4 \pi r^{2} \\\\ &\frac{d S}{d t}=8 \pi r \times \frac{d r}{d t} \end{aligned}

\begin{aligned} &\frac{d r}{d t}=\frac{1}{8 \pi r} \times \frac{d S}{d t} \\\\ &\frac{d r}{d t}=\frac{1}{8 \pi r} \times 2 \quad\left(\frac{d S}{d t}=2(\text { given })\right) \end{aligned}

\begin{aligned} &\frac{d r}{d t}=\frac{1}{8 \pi \times 6} \times 2 \quad(r=6(\text { given })) \\\\ &\frac{d r}{d t}=\frac{1}{24 \pi} \mathrm{cm} / \mathrm{sec} \end{aligned}

Now, Volume of sphere =V=\frac{4}{3} \pi r^{3}

 

\frac{d V}{d t}=4 \pi r^{2} \times \frac{d r}{d t}

Let’s put value of r =6 and  \frac{d r}{d t}=\frac{1}{24 \pi} \mathrm{cm} / \mathrm{sec}

 

\frac{d V}{d t}=4 \pi \times 6^{2} \times \frac{1}{24 \pi}=6 \mathrm{~cm}^{3} / \mathrm{sec}

Posted by

infoexpert26

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question