Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m3. If building of tank costs Rs 70 per sq metres for the base and Rs 45 per square metre for sides. What is the cost of leas

9) A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m3. If building of tank costs Rs 70 per sq metres for the base and Rs 45 per square metre for sides. What is the cost of least expensive tank?

Answers (1)

best_answer

Let l ,  b and h are length , breath and height of tank
Then, volume of tank = l X b X h = 8 m^3
h = 2m (given) 
lb = 4 = l = \frac{4}{b}
Now,
area of base of tank = l X b = 4
area of 4 side walls of tank = hl + hl + hb + hb = 2h(l + b)
Total  area of tank (A) = 4 + 2h(l + b)
A(b) = 4 + 2h(\frac{4}{b}+b)
A^{'}(b) = 2h(\frac{-4}{b^2}+1)\\ A^{'}(b)=0\\ 2h(\frac{-4}{b^2}+1) = 0\\ b^2= 4\\ b = 2
Now,
A^{''}(b) = 2h(\frac{-4\times-2b}{b^3})\\ A^{''}(2) = 8 > 0
Hence, b = 2 is the point of minima
l = \frac{4}{b} = \frac{4}{2} = 2
So, l = 2 , b = 2 and h = 2 m
Area of base =  l X B = 2 X 2 = 4 \ m^2
building of tank costs Rs 70 per sq metres for the base  
Therefore, for 4 \ m^2 Rs = 4 X 70 = 280 Rs
Area of 4 side walls = 2h(l + b)
                                = 2 X 2(2 + 2) = 16 \ m^2
building of tank costs Rs 45 per square metre for sides
Therefore, for 16 \ m^2  Rs = 16 X 45 = 720 Rs
Therefore, total cost for making the tank is = 720 + 280 = 1000 Rs 

Posted by

Gautam harsolia

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 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years
anam-khan

CBSE Class 12 accountancy board exam analysis 2024 out; paper rated easy, balanced

Latest Question