Mathematician makes the perfect cream tea!

Gap-fill exercise

Fill in all the missing numbers, then press "Check" to check your answers. Use the "Hint" button to get a free digit if an answer is giving you trouble. Note that you will lose points if you ask for hints or clues!
Read this first. http://www.itv.com/news/westcountry/2013-05-28/mathematician-cooks-up-perfect-cream-tea-recipe/ Lets test the formulae to see if it gives sensible answers. Say a scone has a radius of 3cm. Calculate the thickness of the clotted cream. Don't forget that r with a 3 after it means r cubed and is calculated as r x r x r. The brackets mean "do that bit first", so you need to subtract 1 fromthe radius, square the answer, then multiply by 8.
Use a calculator and enter the complete answer.
Thickness of clotted cream = (3 x 3 x 3) / 8 x (2 x 2) = cm
What is this to the nearest millimetre? mm
Do you think this is a sensible thickness for the cream?

Now lets calculate the thickness of the jam for the same scone.

Thickness of jam = 3 x 3 x 3 x 3 / 40 x (2.5 x 2.5)= cm
Round this the nearest mm. mm
Do you think this is a sensible thickness for the jam?

Now try a 4cm scone
Thickness of clotted cream = cm (round your answer to 3 decimal places)
What is this to the nearest mm? mm

So the scone is wider and the thickness of cream is slightly .

What is the thickness of jam for a 4cm scone? cm (Round to 3 decimal places)
What is this to the nearest mm? mm

What if we had a very small scone, say with a radius of 1cm? (Don't forget 1 x 1 x 1 = 1 not 3!)
Thickness of cream = 1/0
What is 1 divided by 0?
Can we put an infinite amount of cream on the scone? but we could have fun trying!

Do you think this means the formula should not be trusted?

No, it just means it only works for sensible sizes of scone! Nobody would want to buy a scone that is only 1cm in radius!