Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • need solution for RD Sharma maths class 12 chapter Differentials Errors and Approximations exercise 13.1 question 3

need solution for RD Sharma maths class 12 chapter Differentials Errors and Approximations exercise 13.1 question 3

Answers (1)

Answer: 2 k \pi c m^{2}

Hint: Here, Area of a circular plate of radius  x is given by A=\pi x^{2}

Given: the radius of a circular plate initially is 10 cm and it increase by K%

Solution: Suppose x be the radius of the plate, and \Delta x is the change in the value of x

Thus we have x=10 \text { and } \Delta x=\frac{K}{100} \times 10

So,  \Delta x=0.1 K

Differentiating A with respect to x

\begin{aligned} &\frac{d A}{d x}=\frac{d}{d x}\left(\pi x^{2}\right) \\\\ &\frac{d A}{d x}=\pi \frac{d}{d x}\left(x^{2}\right)=n x^{n-1} \\\\ &\Rightarrow \frac{d A}{d x}=2 \pi x \end{aligned}

\begin{aligned} &\Rightarrow \text { when } x=10 \text { and } \frac{d A}{d x}=2 \pi(10) \text { so, } \frac{d A}{d x}=20 \pi \\\\ &\Rightarrow \Delta y=\frac{d y}{d x} \Delta x \end{aligned}

\begin{aligned} &\text { Here, } \frac{d A}{d x}=20 \pi \text { and } \Delta x=0.1 K \\\\ &\Delta A=(20 \pi)(0.1 K) \\\\ &\Delta A=2 K \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

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