S.chand Class 8 Maths Solution Chapter 19 Graphical Representation of Data Exercise 19 C

 Exercise 19 C

Question 1

Draw pie charts to represent the following information, first working out the angles.

1. The number of books lent out by a school library each day is shown in the following table.

Day	Mon	Tues	Wed	Thurs	Fri
Number of books lent	10	25	33	16	6

2. A student secured marks in different subjects as shown in the following table.

Subjects	English	Computer	Science	Mathematics
Marks	35	40	45	60

3. The number of students in a hostel speaking different languages is given below. Present the data in a pie chart.

Language	Hindi	English	Marathi	Tamil	Bengali	Total
Number of students	40	10	8	8	6	72

4. A pie diagram of the marks secured by a student in Maths, English, Physics and Chemistry is shown here Read the graph and find the marks in Chemistry secured by the student.

<fig>

[Hint: Let the angle of the sector representing the marks in Chemistry be $x$ in degrees.

Then, $100^{\circ}+75^{\circ}+100^{\circ}+x=360^{\circ}$,

$\Rightarrow \quad 275^{\circ}+x=360^{\circ} \Rightarrow x=360^{\circ}-275^{\circ}=85^{\circ}$

Now, A sector of $100^{\circ}$ represents 80 marks (Maths)

$\therefore \quad$ A sector of $1^{\circ}$ represents $\frac{80}{100}$ marks

$\therefore \quad$ A sector of $85^{\circ}$ represents $\frac{80}{100} \times 85=68$ marks

Hence, marks obtained in Chemistry = 68.]

5. A pie chart representing the population of four cities is shown here. Read the pie chart and find the population of the city $D$.

[Hint : Similar to Q. 4]

Multiple Choice Questions (MCQs)

6. The pie chart shows the number of participants of 5 countries $P, Q, R$, $S$ and $T$ taking part in a tennis tournament. Calculate the percentage of participants of country $P$.

<Fig>

(a) $13.5 \%$

(b) $34.7 \%$

(c) $37.5 \%$

(d) $20 \%$

7. A school has a strength of 3000 students. The alongside pie graph shows the interests of students in different subjects. The number of students interested in English is :

(a) 750

(b) 700

(c) 900

(d) 300

<Fig>

S.chand books class 8 maths solution chapter 19 Special Types of Quadrilaterals exercise 19 C

 EXERCISE 19 C

Question 1

For each of the statements given below, indicate if it is true(T) or false(F):
(i) A rectangle is a parallelogram
(ii) A square is a rectangle
(iii) A parallelogram is a rhombus
(iv) A square is a rhombus
(v) A rectangle is a square
(vi) A square is a parallelogram

Sol :

(i) T
(ii) T
(iii) F
(iv) T
(v) F
(vi) T

Question 2

What kind of a quadrilateral is the following ?
The diagonals and the sides form four congruent right-angled triangles.

Sol :

Rhombus

Question 3

PQRS is a quadrilateral. What kind of quadrilateral is it if
(i) PQ is parallel to RS and the diagonals are equal in length ?
(ii) PQ and RS are parallel and ∠P=∠R ?

Sol :

Isosceles trapezium

Question 4

Which of the following are true for a rhombus ?
(i) It has two pairs of parallel sides
(ii) It has two pairs of congruent angles
(iii) It has two pairs of congruent sides
(iv) Two of its angles are right angles
(v) Its diagonals bisect each other and are at right angles
(vi) Its diagonals are congruent and perpendicular
(vii) It has all its sides of equal length

Sol :

(i) T
(ii) T
(iii) T
(iv) F
(v) T
(vi) F
(vii) T

Question 5

The diagonals of a quadrilateral are perpendicular to each other to such a quadrilateral always a rhombus? if your answer is a 'no' , draw a figure to justify answer

Sol :

No, A kite also has this property

Question 6

A window frame has one diagonal longer than the other.Is the window frame a rectangle? Why or why not ?

Sol :

No, diagonals of a rectangle should be equal 

Question 7

What kind of quadrilateral is formed when the mid-points of the sides of the following are joined ?
(i) a rectangle
(ii) a rhombus
(iii) a kite
(iv) an isosceles trapezium

Sol :

(i) Rhombus

(ii) Rectangle

(iii) Rectangle

(iv) Rhombus