Dimensions of special-offer can, given '10% bigger'

[Monkeyseat]

Sorry, not sure where this goes, so move it to the correct forum if neccessary.

15) A standard cylindrical can of Lemfizz holds 400 mL of drink. A special-offer can is advertised as being "10% bigger".

a) Pete thinks that the special-offer can will be an enlargement of the standard can with all the dimensions increased by 10%. Work out the capacity of the special-offer can using Pete's interpretation of the offer.

b) Mike thinks that the special-offer can will be an enlargement of the standard can with the capacity increased by 10%. The height of a standard can is 15 cm. Work out the height of the special-offer can using Mike's interpretation of the offer.

I know it's pretty basic, but I wasn't sure.

I got 440ml for A (400*1.10) and 15.48 for B (used 440ml from A and found the length scale factor from that), but if you could clear it up, that would be great.

Thanks.
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Edited by stapel -- Reason for edit: Replacing (huge) scan with typed-out text.

 

[skeeter]

(a) "all dimensions increased 10%" ...

old volume ... \(\displaystyle \L \pi r^2 h = 400\)

increasing r and h by 10 % ...

new volume ... \(\displaystyle \L \pi (1.1r)^2 (1.1h) = (1.1)^3 \pi r^2 h = (1.1)^3 \cdot 400 = 532.4\), an increase of over 33% in volume.

(b) "capacity increased by 10%" ... new volume is 440 mL

assume that only the height is changed ...

old volume ... \(\displaystyle \L \pi r^2 h = 400\)

new volume \(\displaystyle \L \pi r^2 (kh) = 440\), where k = factor that h is increased

\(\displaystyle \L k = \frac{440}{400} = 1.1\)

new height would be (1.1)(15 cm) = 16.5 cm

 

[Monkeyseat]

Thanks for the reply.

I was just wondering about b, when you divide 440/400 that gives you the volume scale factor then don't you have to cube root it before you multiply it by 15 for the length scale factor?

Thanks.

EDIT:

This is what I mean:



Same question really, but they cube root it...?

 

[skeeter]

(b) "capacity increased by 10%" ... new volume is 440 mL

assume that only the height is changed ...

as I stated, I calculated for a change in the can's height only.

if you are looking to change both the radius and height, and keep the two cans similar, then take the cube root of the scale factor.

the problem, as you posted it, is not clear on which parameter(s) are to be changed.