Area Related to Circles Test

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Area Related to Circles Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

What is name of following shape ?

A
Cylinder

B
Cone

C
Circle

D
Cube

Solution

it is a circle..
Question 2
1 / -0

In the figure, if the length of the arc $$KP = 22cm$$ then KM equals to (O is centre)

A
14 cm

B
28 cm

C
11 cm

D
None

Solution

$$circumference=2\pi r$$
For the arc, $$\angle POK=90^o$$
$$\Rightarrow length\ of\ the\ arc= \dfrac {90}{360}\times 2\pi r=22\Rightarrow r=14$$
diameter $$KM=2r=28 cm$$.
Question 3
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Identify which among the pieces given below will not be requires to complete the square.

A
K

B
H

C
J

D
I

Solution

Among the following we can see that, $$J$$ is not required to complete the square.
By rotating and arranging the pieces $$H, I$$ and $$K$$ we can form a square.
Question 4
1 / -0

From the figure, identify the center of the circle.

A
$$A$$

B
$$D$$

C
$$B$$

D
$$C$$

Solution

Center of a circle is a point inside the circle and is at an equal distance from all of the points on its circumference.
In the given figure, $$C$$ is such point.
So, $$C$$ is the center of the given circle.
Hence, option $$D$$ is correct.
Question 5
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Identify the center of the circle.

A
$$A$$

B
$$O$$

C
$$D$$

D
$$C$$

Solution

Center of a circle is a point inside the circle and is at an equal distance from all of the points on its circumference.
In the given figure, $$O$$ is such point.
So, $$O$$ is the center of the given circle.
Hence, option $$B$$ is correct.
Question 6
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What is the length of arc AB making angle of $$126^0$$ at center of radius $$8$$?

A
$$2.6\displaystyle \pi $$

B
$$5.6\displaystyle \pi $$

C
$$7.6\displaystyle \pi $$

D
$$\displaystyle \frac{1}{2}\pi $$

Solution

Setting a proportion
AB : OB : : 126 : 360
$$\displaystyle \frac{\overline{AB}}{2\pi r}=\frac{126}{360}$$
$$\displaystyle \overline{AB}=\left ( \frac{126}{360} \right )\times 2\pi r$$
$$\displaystyle \overline{AB}=\left ( \frac{126}{360} \right )\times 2\pi \times 8$$
$$\displaystyle \overline{AB}=5.6\pi $$
Question 7
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Two concentric circles intersect at _____ number of points.

A
$$2$$

B
$$0$$

C
$$1$$

D
None of these

Solution

Two concentric circles do not intersect. They only share a common centre as shown in the figure.
Question 8
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Calculate the area of the shaded region of the following figure. $$ABCD$$ is a rectangle having length $$30\ cm$$, breadth $$20\ cm$$. $$E, F$$ and $$G$$ are midpoints of $$AB, CD$$ and $$AD$$ respectively.

A
$$400\ cm^{2}$$

B
$$450\ cm^{2}$$

C
$$375\ cm^{2}$$

D
$$325\ cm^{2}$$

Solution

Area of shaded region $$=$$ Area of rectangle $$-$$ Area of both triangles

A$$_{1} =$$ Area of rectangle $$= 30\times 20 = 600\ cm^{2}$$
A$$_{2} =$$ Area of triangle $$\triangle GDF = 75\ cm^{2}$$
A$$_{3} =$$ Area of triangle $$\triangle GAE = 75\ cm^{2}$$

Area of shaded region $$= 600-75-75 = 450\ cm^{2}$$
Question 9
1 / -0

Which of the following solids has the greatest number of faces?

A

B

C

D

Solution

(A) Number of faces $$= 15$$
(B) Number of faces $$= 9$$
(C) Number of faces $$= 11$$
(D) Number of faces $$= 6$$.
Question 10
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Find the difference of the areas of two segments of a circle formed by a chord of length $$5\ cm$$. Subtending an angle of $$90^{o}$$ till the centre.

A
$$32.14$$ sq. cm

B
$$35.42$$ sq. cm

C
$$38.96$$ sq. cm

D
$$42.43$$ sq. cm

Solution

Let $$r$$ be the radius of circle and $$AB$$ be the chord, which makes $$90^o$$ angle at centre.
$$AB=5cm$$
In right $$\triangle OAB$$, using pythagoras theorem
$$OA^2+OB^2=AB^2 \\ \Rightarrow r^2+r^2=5^2 \\ \Rightarrow 2r^2=25 \\ \Rightarrow r=\cfrac{5}{\sqrt{2}}$$
Area of circle $$=\pi r^2 =\cfrac{22}{7} \times \cfrac{5}{\sqrt{2}} \times \cfrac{5}{\sqrt{2}}=39.28cm^2$$
Area of minor segment $$=Area\; of\; sector - Area \;of\; \triangle OAB \\ =\cfrac{90^o}{360^o}\times \pi r^2 - \cfrac{1}{2} \times \cfrac{5}{\sqrt{2}} \times \cfrac{5}{\sqrt{2}} \\ =\cfrac{1}{4}\times 39.28 - \cfrac{25}{4}=\cfrac{14.28}{4}=3.57cm^2$$
Area of major segment $$=39.28-3.57=35.71 cm^2$$
Required difference $$=35.71-3.57=32.14cm^2$$