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**GCSE** **Mathematics**** Question Analysis Topic: Mathematics - Surface Area**

**Exam Question:**

Of all the closed right circular cylindrical cans of volume 128πcm3, find the dimensions of the can which has minimum surface area.

**Answer:**

For GCSE Mathematics, you should know:

We are given the following:**V = 128****π = πr**^{2}**h --> h = 128 / r**^{2}

Defining surface area S, we have:**S = 2****πrh + 2πr**^{2}

Substituting 128 / r2 into h,

**S(r) = 256π/r + 2πr**^{2}** --> S(r) = -256π/r**^{2}** + 4πr**

For S(r) = 0, -256π/r2 + 4πr --> 4 = 4 cm

At the **minima**, **S(4) > 0 at r = 4**.

And so, h = 128π / π x 4 x 4 = 8 cm

Therefore, **4cm radius **and **8cm height** are the measurements that the can should have for a minimum surface area.

Work hard for your GCSE Mathematics examination!

End of analysis. Great!