Question

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solve question 24

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Answer 1

Answer:

Step-by-step explanation

Volume of tank=8 cubic m

So,

lbh=8

Given h(depth)=2

So lb= 8÷2=4

Since area of base is lb(height has nothing to do with base area) hence it is fixed we can calculate least base area.

So base area = 4 sq m

Now about the sides

We also need to keep area of side less to reduce cost

Area of sides= 2lh+2bh=2h(l+b)

So for min side area we should get min value of l+b

But lb(base area calculated above) is fixed and it is 4.

If we take l=2 and b=2

lb=2×2=4 and l+b=2+2=4 and l+b can't have a value less than 4 for lb=4(fixed)

Let's cross check that,

If we take l=1 and b=4 then lb is 4(which we need) but l+b is 5 which will increase side area

Also if we take l=1/2 and b=8 lb will be 4 but l+b will cross 8

Since we need least l+b value for lb=4(which is proved to be fixed)

Our only option is l=2 and b=2

Lol..turns to be a cube of 2×2×2

Let's find cost

For base

70×4=280

For sides 45×2h(l+b)

=90×2×4=780

Total=780+280= 1060 is the min cost