September 12, 2023
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 = 128π = πr2h --> h = 128 / r2
Defining surface area S, we have:
S = 2πrh + 2πr2
Substituting 128 / r2 into h,
S(r) = 256π/r + 2πr2 --> S(r) = -256π/r2 + 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!