The diagram shows two solid cones which are geometrically similar.
The height of the smaller cone is x cm and that of the larger one is 9 cm.
The volume of the smaller cone is 32 cm³ and the volume of the larger cone is 108 cm³. Calculate the value of x.

In the triangle ABC, AB is parallel to DE.
Angle BAD = 110° and angle ACB = 36°. (a) Given that CE = 3 cm and EB = 2 units.
Calculate the ratio $\frac{\text{area of ABC}}{\text{area of DEC}}$.

A box of fruit juice contains a mixture of apple, orange, pineapple and tropical juices.
The mixture is in the ratio apple : orange : pineapple : tropical = 9 : 7 : 4 : 5.
The box contains 540 millilitres of apple juice.
(a) Find the total amount of fruit juice in the box in litres.

(b) Calculate the amount of tropical juice in the box. Give your answer in millilitres.

(c) 70% of the tropical juice is mango. Calculate the amount of mango juice in the box.

$x:y=3:7$ and $y:z=2:3$
Find the ratio $x:y:z$.

The cubes A and B have volume of 216 cm³ and 64 cm³. Find the ratio:
(a) Height of A : height of B,

(b) Surface area of A : surface area of B.

A farmer harvests 500 bags of corn every year.
He sells $\frac{2}{5}$ of this harvest, keeps 48% as seed and keeps the remaining for his family.
Calculate the number of bags kept for the family.

P varies inversely as a square of r.
When p = 9, r = 2.
(a) Write an expression for p in terms of r.

(b) Find the decrease in p if r is tripled.

(c) v and w are two other quantities such that p is inversely proportional to v and v is inversely proportional to w.
Show that p is directly proportional to w.

t varies inversely as the difference of r² and 7.
t = 9 when r = −2.
(a) Write an equation for t, in terms of r.

(b) It is further given that t = 12 when $r=\frac{\sqrt{a}}{b}$, where a and b are integers.
Find the value of a and the value of b.

Khaola makes a map of Mafeteng and uses a scale of 1 : 50 000.
The area of a village on his map is 8 cm².
Calculate, in square kilometres, the actual area of the village.

(a) y is inversely proportional to x³.
When y = 9, x = 3.
Find y when x = 10.

(b) p is proportional to q².
Find the percentage increase in the value of p when q is increased by 50%.

x is inversely proportional to (y − 2).
When y = 6, x = 9.
Find the value of x when y = 20.

p is inversely proportional to q².
Given that p = 24 for a particular value of q,
Find the value of p when q is doubled.

Temperatures at 04 00 hours and 12 00 hours were −5°C and 19°C, respectively.
(a) Find the difference between the two temperatures.

(b) Assuming that the temperature was rising at a steady rate, find:
(i) The temperature at 09 30 hours,

(ii) The time when the temperature was 8°C.