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Functions and Their Properties · Paper 2 — Free Maths AI HL Practice Questions

1MasterySAQ-SDefinition and types of functions (one-to-one, onto etc.)6 marksPaper 2~9 min

A company manufactures cylindrical containers with a fixed volume of

1000\,\text{cm}^3

. The cost of the material for the curved surface is

0.50

dollars per

\text{cm}^2

, and the cost for the two circular ends is

0.80

dollars per

\text{cm}^2

(a)

Show that the total cost,

C

dollars, can be expressed as

C = \frac{1000}{r} + 1.6\pi r^2

where

r\,\text{cm}

is the radius of the cylinder. [3 marks]

(b)

Calculate the value of

r

that minimises the total cost. Give your answer correct to 3 significant figures. [2 marks]

(c)

Hence determine the minimum total cost and justify that this value of

r

gives a minimum rather than a maximum. [1 mark]

Solutions

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