CIE Mathematics Paper-1: Specimen Questions 17 - 18 of 175

Question number: 17

Essay Question▾

Describe in Detail

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

the cube of side in the diagram.

the cube of side in the diagram.

Find the below given calculations by using given values of cube.

(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: 6a2=6×62=216cm2

(b) Volume of the cube: a3=63=216cm3

Now, 106cm=1meter3

So, 216cm3=?meter3

So, 216106=216×106meter3

Question number: 18

Essay Question▾

Describe in Detail

Solve

Two triangles made by side splitter theorem

Two triangles made by side splitter theorem

Find the below given calculations using given lengths and angles

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 = 680 . 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 ABBD=ACCE .

So, Triangle ABC is similar to triangle ADE.

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

Now, ABC=680ADE=680(BCDE)

So, for ABC,cos680=BCAB.(I)

For ADE,cos680=ADDE.(II)

So, from (I) and (II),

BCAB=ADDE812=AD10AD=8×1012=203=6.67cm

(c) Angle ABC = 680 . So, size of the reflex angle at D is similar to angle ABC because BCDE and so both triangles are similar.

So, size of reflex angle at D is 680.

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