OCR C1 2006 June — Question 8

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2006
SessionJune
TopicDifferentiation Applications
TypeOptimization with constraints

8 A cuboid has a volume of \(8 \mathrm {~m} ^ { 3 }\). The base of the cuboid is square with sides of length \(x\) metres. The surface area of the cuboid is \(A \mathrm {~m} ^ { 2 }\).
  1. Show that \(A = 2 x ^ { 2 } + \frac { 32 } { x }\).
  2. Find \(\frac { \mathrm { d } A } { \mathrm {~d} x }\).
  3. Find the value of \(x\) which gives the smallest surface area of the cuboid, justifying your answer.