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1 Unit AS 1: Pure Mathematics

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Question 189

A precision-engineered storage vault for high-density alloys is in the shape of a cuboid with a rectangular base of width xxx cm and length 3x3x3x cm. The height of the vault is hhh cm.

The volume of the vault is fixed at 1350 cm31350\text{ cm}^31350 cm3.

a.

Show that the surface area of the vault, S cm2S\text{ cm}^2S cm2, is given by

S=6x2+3600x S = 6x^2 + \frac{3600}{x} S=6x2+x3600​
[4]
b.

Find dSdx\frac{dS}{dx}dxdS​.

[2]
c.

Hence find the value of xxx for which SSS is stationary, giving your answer to 3 significant figures.

[3]
d.

Find d2Sdx2\frac{d^2S}{dx^2}dx2d2S​ and hence show that the value of xxx found in part (c) gives the minimum value of SSS.

[3]
e.

Hence find the minimum surface area of the vault, giving your answer to 1 decimal place.

[2]
Markscheme

1 Unit AS 1: Pure Mathematics Questions

  1. A Level
  2. /Maths
  3. /1 Unit AS 1: Pure Mathematics

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