Bài tập CALCULUS 78

Created by T. Madas
Question 262

(****+)

y

y = ( x − 4)

C

B

A

2

y=4

x

O

The diagram above shows the curve with equation
2

y = ( x − 4) , x ∈ » ,

intersected by the straight line with equation y = 4 , at the points A and B .
The curve meets the y axis at the point C .
Calculate the exact area of the shaded region, bounded by the curve and the straight

line segments AB and BC .

C2P , area = 76
3

Created by T. Madas


Created by T. Madas
Question 263

(****+)

x cm
2 cm

x cm

The figure above shows the design of coffee jar with a “push on” lid.
The jar is in the shape of a right circular cylinder of radius x cm . It is fitted with a lid
of width 2 cm , which fits tightly on the top of the jar, so it may be assumed that it has
the same radius as the jar.
The jar and its lid is made of sheet metal and there is no wastage.
The total metal used to make the jar and its lid is 190π cm 2 .
(This figure does not include the handle of the lid which is made of different material.)

a) Show that volume of the jar, V cm3 , is given by

(

)

V = π 95 x − 2 x 2 − x3 .

b) Determine by differentiation the value of x for which V is stationary.

[continues overleaf]

Created by T. Madas


Created by T. Madas
[continued from overleaf]

c) Show that the value of x found in part (b) gives the maximum value for V .
d) Hence determine the maximum volume of the jar.

MP1-X , x = 5 cm , Vmax = 300π ≈ 942 cm3

Created by T. Madas