Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

The edge of a cube was found to be $30cm$ with a possible error in mesurement of $ 0.1cm$. Use differentials to estimate the maximum possible error in computing the surfacearea of the cube .

This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com

1 Answer

Comment
A)
Toolbox:
  • Let $y=f(x)$ be a differentiable function then the quantities $dx$ and $dy$ are called differentials.The differential $dx$ is an independent variable.
  • The differential $dy$ is then defined by $dy=f'(x)dx(dx \approx \Delta x)$
  • Also $f(x+\Delta x)-f(x)=\Delta y =dy $ from which $f(x+\Delta x) $can be evaluated
Step 1:
The surface area of the cube
$s=6x^2$
$ds=12 x dx$
Step 2:
When $x=30,dx \approx \Delta x =0.1$
$\therefore ds=12 \times 30 \times 0.1=36 cm^2$
The maximum error is $ds=36 cm^2$
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...