Chapter(^7)
● P1
? (Page 209)
1 (i) A cylinder
(ii) A sphere
(iii) A torus
2 73 π
●^ (Page^ 211)
Follow the same procedure as that
on page 209 but with the solid sliced
into horizontal rather than vertical
discs.
Exercise 6H (Page 212)
1 For example: ball, top (as in
top & whip), roll of sticky tape,
pepper mill, bottle of wine/milk
etc., tin of soup
2 (i)
1043 π units^3
(ii)
563 π units^3
(iii)
56
15
π
units^3
(iv)
8 π units^3
3 (i) (ii)
(iii) 12 π units^3
4 (i)
7 π units^3
(ii)
234 π units^3
(iii)
18 π units^3
5 (i)
(ii) 45.9 litres
6 (i)
(ii) (^) ∫^120 π(y + 4) dy
(iii) 3 litres
(iv) (^) ∫^100 π(y + 4) dy = 90 π
= 34 of 120π
7 42 π
8 6
Chapter 7
●?^ (Page^ 219)
When looking at the gradient of a
tangent to a curve it was considered
as the limit of a chord as the
width of the chord tended to zero.
Similarly, the region between a
curve and an axis was considered as
the limit of a series of rectangles as
the width of the rectangles tended
to zero.
Exercise 7A (Page 221)
1 (i) Converse of Pythagoras’
theorem
(ii) 178 ,,^1517158
3 (i) 5 cm
O x
y
y = x
O 2 x
y
y = x + 2
2
O x
y y = x (^2) + 1
–1 1
1
O x
y
4
y = x
3
O x
y
4 y = 3x
4
(4, 3)
O x
y
y = 3x
3
6
O x
y
3
y = x – 3
–3
O x
y
y = x^2 – 2
4
–2
y
x
62.5
O 10 25
y = 10 10
(base)
O x
y
12 y x^2 –4
–4
–2 2
R