Area Related to Circles Test

Result

Area Related to Circles Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

The length of an arc of a sector of a circle of radius r units and of centre angle $$\theta$$ is $$\displaystyle \frac{\theta}{360^{\circ}} \times \pi r^2$$.

A
True

B
False

C
Neither

D
Either

Solution

Length of arc subtending angle $$\theta$$ = $$\frac{\theta}{360} \times 2 \pi r $$. Note that area will have the dimension of square of length. So $$\frac{\theta}{360} \times \pi r^{2} $$, cannot be the length.
Question 2
1 / -0

If an arc of a circle of radius $$14\ cm$$ subtends an angle of $$60^{\circ}$$ at the centre, then the length of the arc is $$\displaystyle \dfrac{44}{3}\ cm$$.

A
True

B
False

C
Niether

D
Either
Question 3
1 / -0

In a circle of radius 21 cm, an arc subtends an angle of $$60^{\circ}$$ at the centre the length of the arc is 22 cm.

A
True

B
False

C
Neither

D
Either

Solution

Arc length = $$\frac{\theta}{360} \times 2 \pi r = \frac{60}{360} \times 2 \times \frac{22}{7} \times 21 = 22 cm.$$
Question 4
1 / -0

A wire in the form of circle of diameter 42 cm is cut and bent to form a square. The side of the square is

A
16 cm

B
17 cm

C
33 cm

D
16.5 cm

Solution

Perimeter of square = Circumference of circle

$$\displaystyle 4\times side=\frac{22}{7}\times d$$ where $$d$$ is diameter.

$$\displaystyle 4\times side=\frac{22}{7}\times 42=132$$

$$\displaystyle \Rightarrow side=33\ cm$$
Question 5
1 / -0

A set of points equidistant from a fixed point in a plane figure is called

A
triangle

B
circle

C
square

D
none of these

Solution

A set of points equidistant from a fixed point in a plane figure is called a circle where the distance between each of the set of the points and the fixed point forms the radius of the circle.
Question 6
1 / -0

The circumference of a circular playground is 528 m. Find the total expenditure of repairs of the ground at the rate of Rs. 1.50 per square metre $$\displaystyle (\pi = \frac{22}{7})$$

A
33264

B
33345

C
33456

D
none of these

Solution

Perimeter of the playground$$=528 m$$
$$=>2\pi r=528$$
$$=>r=\dfrac{528\times 7}{22\times 2}$$
$$=>r=84$$
Now, Area of the playground$$=\pi r^2$$
$$=\dfrac{22}{7}\times 84\times 84$$
$$=22176m$$
Therefore,
Total expenditure$$=area\times 1.50$$
$$=22176\times 1.50$$
$$=33264$$
Question 7
1 / -0

Fixed point in the circle is called _____ of the circle.

A
radius

B
centre

C
diameter

D
none

Solution

A circle is the set of all those point in a plane whose distance from a fixed point remains constant. Then, this fixed point is called the centre of the circle.
Hence, option $$B$$ is correct.
Question 8
1 / -0

If the length of the largest chord of a circle is $$17$$ cm, find the radius of a circle.

A
$$34$$ cm

B
$$8.5$$ cm

C
$$ \sqrt { 17 } $$ cm

D
$$ \sqrt { 34 } $$ cm

Solution

Given, the largest chord of a circle $$=17cm$$.
We know that the largest chord of a circle is its diameter.
$$\therefore$$ The diameter of the given circle $$=17 cm$$.
Hence, radius of the same circle$$=\dfrac { \text {diameter} }{ 2 } =\dfrac { 17 }{ 2 } cm=8.5cm$$.
Therefore, option $$B$$ is correct.
Question 9
1 / -0

In a circle of radius 21 cm an arc subtends an angle of $$\displaystyle 56^{\circ} $$ at the centre of the circle. The length of the arc is

A
$$20.53$$ cm

B
$$17.53$$ cm

C
$$15.53$$ cm

D
$$16.53$$ cm

Solution

$$\displaystyle \theta =56^{\circ},r=21cm$$
Length. of $$\displaystyle AB=\dfrac{56^{\circ}}{360^{\circ}}\times 2\times \dfrac{22}{7}\times 21$$
$$\displaystyle =\dfrac{616}{30}=20.53cm$$
Question 10
1 / -0

In the given figure, find the area of the unshaded portion within the rectangle.

A
11.27 $$cm^2$$

B
13.27 $$cm^2$$

C
17.27 $$cm^2$$

D
19.27 $$cm^2$$

Solution

Area of a circle $$=\pi r^2$$
$$=\frac{22}{7} \times 3 \times 3$$
$$=28.29cm^2$$
$$\therefore$$ Area of the shaded region $$=28.29+28.29+\frac{28.29}{2}$$
$$=70.73cm^2$$
Area of the rectangle $$=15\times 6=90cm^2$$
$$\therefore$$ Area of the unshaded region $$=(90-70.73)cm^2$$
$$=19.27cm^2$$

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Re-Attempt Weekly Quiz Competition

Area Related to Circles Test - 16

Result

Area Related to Circles Test - 16

Score

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SHARING IS CARING

Question 1

True

False

Neither

Either

Solution

Question 2

True

False

Niether

Either

Question 3

True

False

Neither

Either

Solution

Question 4

16 cm

17 cm

33 cm

16.5 cm

Solution

Question 5

triangle

circle

square

none of these

Solution

Question 6

33264

33345

33456

none of these

Solution

Question 7

radius

centre

diameter

none

Solution

Question 8

$$34$$ cm

$$8.5$$ cm

$$ \sqrt { 17 } $$ cm

$$ \sqrt { 34 } $$ cm

Solution

Question 9

$$20.53$$ cm

$$17.53$$ cm

$$15.53$$ cm

$$16.53$$ cm

Solution

Question 10

11.27 $$cm^2$$

13.27 $$cm^2$$

17.27 $$cm^2$$

19.27 $$cm^2$$

Solution

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