4 . A closed rectangular box has length 4x cm , width 2x cm and height y cm , where x , y � 0. It is given that the sum of the length and the height of the rectangular box is 20 cm .
( a ) Write down
( i ) an expression for y in terms of x ;
( ii ) the possible range of values of x .
( b ) Express V in terms of x , where box .
( c ) Using the graphic display calculator to find
( i ) the maximum volume ;
( ii ) the value of x when V attains its maximum ;
( iii ) the value of y when V attains its maximum .
( d ) Express A in terms of x , where
[ 2 ]
3
V cm is the volume of the rectangular
2
A cm is the total surface area of the rectangular box . [ 2 ]
( e ) Someone claims that the total surface area of the box attains its maximum when its volume attains its maximum . Explain why the claim is incorrect . [ 2 ]
[ 2 ]
[ 5 ]
© SE Production Limited 14 All Rights Reserved 2021