# IGCSE Mathematics Paper-1: Specimen Questions with Answers 17 - 20 of 324

## Question 17

### Describe in Detail

Essay▾

The diagram shows a cube of side ‘a’ of 6 cm.

(a) Calculate the area of the cube.

(b) Calculate the volume of the cube in meter.

### Explanation

Here, side a = 6 cm.

(a) Area of cube:

(b) Volume of the cube:

Now,

So,

So,

## Question 18

### Describe in Detail

Essay▾

Solve

In the diagram BC is parallel to DE.

(a) Complete the following statement; Triangle ABC is ________ to triangle ADE.

(b) AB = 12 cm, BC = 8 cm and DE = 10 cm. Find length of AD.

(c) Angle ABC = . Find size of the reflex angle at D.

### Explanation

Here,

(a) BC is parallel to DE, which means it is a side splitter theorem.

In which .

So, Triangle ABC is similar to triangle ADE.

(b) AB = 12 cm, BC = 8 cm and DE = 10 cm.

Now,

So, for

For

So, from (I) and (II) ,

(c) Angle ABC = . So, size of the reflex angle at D is similar to angle ABC because and so both triangles are similar.

So, size of reflex angle at D is

## Question 19

### Write in Short

Solve the equations

(a) ,

(b)

Here,

(a)

(b)

## Question 20

### Describe in Detail

Essay▾

The population of a city is . It is expected that this population will increase by 42% by the year 2,008. Calculate the expected population in 2,008.

### Explanation

Here, Population is .

Expected population will increase by 42% .

So, increment in population will: .

So, expected population will be