Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class12 chapter Maxima and Minima exercise 17.5 question 24 maths.

Explain solution RD Sharma class12 chapter Maxima and Minima exercise 17.5 question 24 maths.

Answers (1)

l =12

Hint: For maxima or minima f'(x) must be zero f'(x) = 0

Given: Let l,b,v be length, breadth and volume

Solution:

2(l+b)=36

l =18-b                 .....(1)

V= \pi l^2 b

V= \pi (18-b)^2 b                    ..... from (1)

\begin{aligned} &=\pi\left(324 b+b^{3}-36 b^{2}\right) \\ &\frac{d V}{d b}=\pi\left(324+3 b^{2}-72 b\right) \\ &\frac{d V}{d b}=0 \end{aligned}

\begin{aligned} &\pi\left(324+3 b^{2}-72 b\right)=0 \\ &324+3 b^{2}-72 b=0 \\ &b^{2}-24 b+108=0 \\ &b^{2}-6 b-18 b+108=0 \\ &(b-6)(b-18)=0 \\ &b=6,18 \end{aligned}

Now,

\begin{aligned} &\frac{d^{2} V}{d b^{2}}=\pi(6 b-72) \\ &\text { At } b=6 \\ &\frac{d^{2} V}{d b^{2}}=\pi(36-72)=-36 \pi<0 \\ &\text { At } b=18 \\ &\frac{d^{2} V}{d b^{2}}=\pi(18 \times 6-72)=36 \pi>0 \end{aligned}

Substitute the value of  b in (1)

l=18-6=12

So, the volume is maximum when a = 12cm and b = 6cm 

 

 

 

Posted by

infoexpert24

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