Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • provide solution for RD Sharma maths class 12 chapter Derivative As a Rate Measure exercise 12.2 question 6

provide solution for RD Sharma maths class 12 chapter Derivative As a Rate Measure exercise  12.2 question 6

Answers (1)

best_answer

Answer: \frac{d r}{d t}=\frac{1}{\pi} \mathrm{cm} / \mathrm{sec}

Hint: We know that the volume of the spherical balloon is V=\frac{4}{3}\pi r^{3} .

Given: The spherical balloon inflated by pumping in 900 cubic cm of gas per second.

Solution: Suppose the radius of the given spherical balloon be r cm and let V be the volume of the spherical balloon at any instant time.

The balloon is inflated by pumping 900 cubic cm of gas per second hence the rate of volume of spherical balloon is increased by,

\frac{\mathrm{d} \mathrm{V}}{\mathrm{dt}}=900 \mathrm{~cm}^{3} / \mathrm{sec} 

\frac{d V}{d t}=\frac{d\left(\frac{4}{3} \pi r^{3}\right)}{d t}                                   \therefore\left(V=\frac{4}{3} \pi r^{3}\right)                                                

lets put value of \frac{d V}{d t}=900(given)

Let’s differentiate \left(\frac{4}{3} \pi r^{3}\right)  w.r.t time

\begin{gathered} 900=\frac{4 \times 3}{3} \times \pi r^{2} \frac{d r}{d t} \\\\ 900=4 \pi r^{2} \frac{d r}{d t} \end{gathered}

So, lets put value of r= 15 (given)

\begin{aligned} &\Rightarrow 900=4 \pi \times 15 \times 15 \times \frac{d r}{d t} \\\\ &\Rightarrow 900=900 \pi \times \frac{d r}{d t} \\\\ &\Rightarrow \frac{900}{900 \pi}=\frac{d r}{d t} \end{aligned}

\begin{aligned} &\Rightarrow \frac{1}{\pi}=\frac{d r}{d t} \\\\ &\text { So, } \frac{d r}{d t}=\frac{1}{\pi} \end{aligned}

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

CBSE Class 10, 12 compartment 2024 exams today for 2.5 lakh students; exam timings, guidelines
anam-khan

CBSE compartment admit card 2024 out at cbse.gov.in; exams from July 15
anam-khan

Reports saying CBSE cannot conduct board exams twice a year currently ‘totally incorrect’; board denies claims

Latest Question