maths! intermediate 2 credit teejay textbook

[_sophie_]

ok, i am so confused right now!
here's the question:
the diagram shows two bottles of Grape & Redcurrant Juice. The two bottles are similar and the cost of the juice depends only on the volume of liquid in the bottle.
If the small one costs �2.50, what should the large one cost?
(There is a drawing of two bottles, one with a length of 10cm, the other a length of 14cm)
how do i do this?!
surely, the linear scale factor is 1.4, and then you cube this? which would be 2.744, and then, do you just do the original price (�2.50) mulitplied by 1.4? or do you need to work out the volumes first? there is no original volume given of the old shape.

thanks :)

[Buenchico]

You actually seem to know how to answer the question but you've simply not got the confidence to apply your answer!

As you've stated, the ratio of the linear measurements is 1.4 to 1

As you've also correctly stated, the ratio of the volumes is found by cubing the linear ratio. So the ratio of the volumes is 2.744 to 1 (i.e. the volume of juice in the bigger bottle is 2.744 times that of the volume in the smaller one).

So the price of the larger bottle must be 2.744 x �2.50 = �6.86

Chris

[_sophie_]

haha thankyou! i got the answer eventually, so thanks for confirming it :)