Angle subtended by arc - class-VIII

Question 1 Multiple Choice (Single Answer)

State true or false.

Sector is the region between the chord and its corresponding arc.

True
False

Question 2 Multiple Choice (Single Answer)

$r$ is the radius and $l$ is the length of an arc. The area of a sector is ______.

$\dfrac { 1 } { 2 } r l$
$\dfrac { 3 } { 2 } r ^ { 2 } l$
$\dfrac { 4 } { 3 } r l$
$\dfrac { 3 } { 2 } r l$

Question 3 Multiple Choice (Single Answer)

State true or false:

Sector is the region between the chord and its corresponding arc.

False
True
cannot be determined
none of the above

Question 4 Multiple Choice (Single Answer)

Say true or false:

A sector is a region between the chord and its corresponding arc.

True
False

Question 5 Multiple Choice (Single Answer)

A circular disc of radius $10 cm$ is divided into sectors with angles $120^o$ and $150^o$, then the ratio of the area of two sectors is

$4 : 5$
$5 : 4$
$2 : 1$
$8 : 7$

Question 6 Multiple Choice (Single Answer)

The region between an arc and two radii joining the centre to the end points of the arc is called

sector
segment
semicircle
non of these

Question 7 Multiple Choice (Single Answer)

$\triangle ABC$ is inscribed in a circle. Point $P$ lies between $A$ and $C$, whereas point $Q$ lies between $B$ and $C$. If $m(\text{arc}\, APC) = 60^\circ$ and $\angle BAC = 80^\circ$, find $m(\text{arc}\, BQC)$.

$180^\circ$
$90^\circ$
$160^\circ$
$120^\circ$

Question 8 Multiple Choice (Single Answer)

Which of the following is not a sector of a circle?

Pizza slice
Cathedral window
Birthday cap
Apple pie

Question 9 Multiple Choice (Single Answer)

Circular dome is a 3D example of which kind of sector of the circle?

Quadrant
Semicircle
Octant
Sextant

Question 10 Multiple Choice (Single Answer)

Points $A,B,C $ are on a circle, such that $m(arc AB)=m(arc BC)=^o$. No point, except point $B$, is common to the arcs.which is the type of $\triangle ABC$?

Equilateral triangle
Scalene triangle
Right angled triangle
Isosceles triangle

Question 11 Multiple Choice (Single Answer)

Find the area of a sector of a circle with radius $6$cm if angle of the sector is $60^o$.

$6\pi$
$7\pi$
$3\pi$
$5\pi$

Question 12 Multiple Choice (Single Answer)

Consider a circle with unit radius. There are seven adjacent sectors, $S _1, S _2, S _3, ............ S _7$, in the circle such that their total area is $\dfrac {1}{8}$ of the area of the circle. Further, the area of the $j^{th}$ sector is twice that of the $(j-1)^{th}$ sector, for $j$ $=$ $2, ........... 7$. What is the area of sector $S _1?$

$\displaystyle \frac{\pi }{508}$
$\displaystyle \frac{\pi }{2040}$
$\displaystyle \frac{\pi }{1016}$
$\displaystyle \frac{\pi }{1524}$

Question 13 Multiple Choice (Single Answer)

The angle subtended by the chord AB in the minor arc of S is -

$\dfrac{3 \pi}{4}$
$\dfrac{5 \pi}{6}$
$\dfrac{2 \pi}{3}$
$\dfrac{ \pi}{4}$

Question 14 Multiple Choice (Single Answer)

The length of minor arc $\overset{\frown}{AB}$ of a circle is $\dfrac{1}{4}$ of its circumference, then the measure of the angle subtended by the minor arc $\overset{\frown}{AB}$ will be ....

30
45
90
60

Question 15 Multiple Choice (Single Answer)

With a given centre and a given radius,only one circle can be drawn.

True
False

Question 16 Multiple Choice (Single Answer)

If angle of sector is $x^o$, then formula used to calculate area is

$\dfrac{x^o}{360}\times \pi r^2$
$2\dfrac{x^o}{360}\times \pi r$
$\dfrac{x^o}{180}\times \pi r^2$
$2\dfrac{x^o}{360}\times r^2$

Question 17 Multiple Choice (Single Answer)

If the circumference of a circle is $8$ units and arc length of major sector is $5$ units then find the length of minor sector.

$3$ units
$5$ units
$7$ units
None of these

Question 18 Multiple Choice (Single Answer)

The angle subtended at the centre of a circle of radius $3cm$ by an arc of length $1cm$ is:

$\cfrac { { 30 }^{ o } }{ \pi } $
$\cfrac { { 60 }^{ o } }{ \pi } $
${ 60 }^{ o }$
None of the above

Question 19 Multiple Choice (Single Answer)

Write True or False:

The tangent to the circumcircle of an isosceles $\triangle ABC$ at A, in which $AB = AC$, is parallel to BC.

True
False
Ambiguous
Data insufficient

Question 20 Multiple Choice (Single Answer)

In $\bigodot (P, 6)$, the length of an arc is $\pi$. Then the arc subtends an angle of measure ___at the center.

30
60
90
120

Angle subtended by arc - class-VIII

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