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# IGCSE question, upper and lower bounds

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1. Q) The volume of a cuboid is 878cm^3, correct to the nearest cubic centimetre
The length of the base of the cuboid is 7cm, correct to the nearest cm.
The width of the base of the cuboid is 6cm, correct to the nearest cm.

Calculate the lower bound for the height of the cuboid.

6.5<= L < 7.5
5.5<= W < 6.5
877.5<= V < 878.5

I thought that the lower bound for the volume must be product of the lower bounds for length, width and height.

6.5x5.5xh = 877.5

h = 877.5 / (6.5x5.5) = 24.5454545454...

but the mark scheme says it's 18 here:

why would the lower bound for the height come from the upper bounds of the length and width?
2. (Original post by SuchBants)
Q) The volume of a cuboid is 878cm^3, correct to the nearest cubic centimetre
The length of the base of the cuboid is 7cm, correct to the nearest cm.
The width of the base of the cuboid is 6cm, correct to the nearest cm.

Calculate the lower bound for the height of the cuboid.
I thought that the lower bound for the volume must be product of the lower bounds for length, width and height

This is correct. But the question asks for the lower bound of the height, not the lower bound of the volume.

The first thing you should do with questions like this is write the formula with the variable that you are maximising/minimising as the subject:

Now think about what V, l and w need to be to give the lower bound of h.

Post your working/ideas if you get stuck.
3. (Original post by notnek)
I thought that the lower bound for the volume must be product of the lower bounds for length, width and height

This is correct. But the question asks for the lower bound of the height, not the lower bound of the volume.

The first thing you should do with questions like this is write the formula with the variable that you are maximising/minimising as the subject:

Now think about what V, l and w need to be to give the lower bound of h.

Post your working/ideas if you get stuck.
I understand from that working out how to get 18.

But i can't see what is incorrect about the lower bound for the volume being:
877.5 = 6.5 x 5.5 x h
That is correct if you use the lower bound for h surely?
Why doesnt it then follow that
877.5/(6.5x5.5) = h
4. (Original post by SuchBants)
I understand from that working out how to get 18.

But i can't see what is incorrect about the lower bound for the volume being:
877.5 = 6.5 x 5.5 x h
That is correct if you use the lower bound for h surely?
Why doesnt it then follow that
877.5/(6.5x5.5) = h
From you trying this method you should have been able to see that it leads to the wrong answer.

If you're trying to minimise a product then you take the lower bound of the two variables in the product:

If you rearrange this

But this is incorrect.

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