Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Application of Derivatives
0 votes

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square in cms to be cut off so that the volume of the box is maximum ?

Can you answer this question?

1 Answer

0 votes
  • Volume of the box=$l\times b\times h$
  • $\large\frac{d}{dx}$$(xy)=x.\large\frac{d}{dx}$$(y)+y.\large\frac{d}{dx}$$(x)$
Step 1:
Side of the square $\rightarrow (45-2x)(24-2x)x$
Volume of the box=$l\times b\times h$
Differentiating with respect to x we get
$\quad=2\times 6(x^2-23x+90)$
Step 2:
For maxima & minima
Step 3:
But $x$ cannot be greater than 12
$\Rightarrow x=5$
Substitute the value of $x=5$ in (1)
$\large\frac{d^2V}{dx^2}=$$12(2\times 5-23)$
$\Rightarrow$ -ve
$\therefore V$ is maximum at $x=5$
(i.e) Square of side 5 cm is cut off from each corner.
answered Aug 8, 2013 by sreemathi.v
edited Aug 19, 2013 by sharmaaparna1

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App