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CBSE Questions for Class 7 Maths Perimeter And Area Quiz 2 - MCQExams.com
CBSE
Class 7 Maths
Perimeter And Area
Quiz 2
The radius of a circle whose area is equal to the sum of the areas of two circles of radii 5 cm and 12 cm is
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13 cm
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14 cm
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15 cm
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17 cm
Explanation
We know that area of a circle of radius $$r = πr ^2 $$
By given condition,
$${ A }_{ 3 }={ A }_{ 1 }+{ A }_{ 2 }$$ .....(1)
Since, $$r_1 = 5$$ & $$r_2= 12$$
So, by (1), we have
$$ { \pi r }^{ 2 }={ \pi 5 }^{ 2 }+{ \pi 12 }^{ 2 }\\\\ { r }^{ 2 }={ 5 }^{ 2 }+{ 12 }^{ 2 }\\\\ r=\sqrt { 25+144 } =\sqrt { 169 } =13 \text{ cm}$$
The radius of a circle is increased by 1 cm. Then the ratio of new circumference to the new diameter is
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$$\pi :3$$
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$$\pi :2$$
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$$\pi :1$$
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$$\pi :\frac { 1 }{ 2 } $$
Explanation
New radius = $$(r+1)\ \mathrm{cm} $$
Ratio = $$2\pi (r+1):2(r+1)=\pi :1$$
If the perimeter and area of a circle are numerically equal then the radius of the circle is
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$$6$$ units
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$$\displaystyle \pi $$ units
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$$4$$ units
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$$2$$ units
Explanation
$$\textbf{Step 1: Substitute area of circle and perimeter of circle formula in the given condition}$$
$$\text{Area of circle}=\pi r^2$$
$$\text{Perimeter of circle}=2\pi r$$
$$\text{Given that area and perimeter are numerically equal}$$
$$\implies \pi r^2=2\pi r$$
$$\implies r=2$$
$$\textbf{Thus, the required radius of the circle is 2 units}$$
From a square metal sheet of side $$28\;cm$$, a circular sheet is cut off. Find the radius of the largest possible circular sheet that can be cut. Also find the area of the remaining sheet.
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$$14\;cm,\;148\;cm^2$$.
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$$14\;cm,\;168\;cm^2$$.
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$$12\;cm,\;168\;cm^2$$.
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$$14\;cm,\;164\;cm^2$$.
Explanation
Area of square sheet $$=$$ $${ (28) }^{ 2 }=784{ cm }^{ 2 }$$
The largest circle of diameter equals to the side of square can be cut off from the square sheet.
$$\therefore $$ Radius of circular sheet $$=$$ $$\dfrac { 28 }{ 2 } =14cm$$
Area of remaining sheet $$=$$ $$784-\pi { r }^{ 2 }=784-\dfrac { 22 }{ 7 } \times 14\times 14$$
$$=$$ $$784 - 616$$ = $$168$$$${ cm }^{ 2 }$$
The difference in the area of a square of perimeter $$88$$ m and a circle with same circumference is
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166 $$\displaystyle cm^{2}$$
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122 $$\displaystyle cm^{2}$$
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133 $$\displaystyle cm^{2}$$
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132 $$\displaystyle cm^{2}$$
Explanation
Perimeter of $$sq=88 cm$$
$$\displaystyle \therefore $$ side of $$sq = 22 cm$$
$$\displaystyle \Rightarrow $$ area of sq $$\displaystyle =484 cm^{2}$$
$$\displaystyle C=2\pi r=88\Rightarrow r=14$$
$$\displaystyle \therefore Area=\dfrac{22}{7}\times 14\times 14=616cm^{2}$$
Difference in the areas $$\displaystyle =616-484=132 cm^{2}$$
The ratio of the outer and inner circumferences of a circular path is $$23:22$$, If the path is $$5\ m$$ wide, the radius of the inner circle is:
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$$55\ m$$
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$$110\ m$$
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$$220\ m$$
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$$230\ m$$
Explanation
Let R and r be the outer and inner radii of the circular path.
Given that,
$$\frac{2\pi R}{2\pi r}=\frac{23}{22}$$
$$=>\frac{R}{r}=\frac{23}{22}$$
Let $$R=23x$$ and $$r=22x$$
It is given that the width of the path is $$5$$m wide
$$\therefore R-r=5$$m
$$=>23x-22x=5$$
$$=>x=5$$
$$\therefore$$ the inner radius of the circle is
$$=22\times 5$$
$$=110$$m
The radius of a circle whose area is equal to the sum of the areas of two circles of radii 3 cm and 4 cm is
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5 cm
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5.5 cm
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5.8 cm
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6 cm
Explanation
The area of circle $$C_1$$ whose radius is $$4\ cm =\pi (4)^{2}$$
$$=16\pi $$ sq cm
And the
area of circle $$C_2$$ whose radius is $$3\ cm = \pi (3)^{2}$$
$$=9\pi $$ sq cm
Given: Area of the new circle is equal to the sum of areas of circles $$C_1$$ and $$C_2$$
Let the radius of the new circle be $$R$$ cm
Area of big circle $$=16\pi +9\pi =25\pi $$ sq cm
$$\Rightarrow$$ $$\pi R^{2}=25\pi$$
$$ \Rightarrow$$ $$R^{2}=25$$
$$\Rightarrow$$ $$R=5$$ cm
So the radius of the new circle $$=5$$ cm
Area of a square 625 sq m. Then the measure of its side is
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$$15$$ m
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$$25$$ m
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$$20$$ m
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$$24$$ m
Explanation
We know that,
Area$$=side\times side$$
$$s \displaystyle \times s \displaystyle= 625 \displaystyle m^{2} $$
$$ s \displaystyle \times s \displaystyle = 25 \displaystyle \times 25$$ $$\displaystyle= $$ 625 $$\displaystyle m^{2} $$
$$s \displaystyle = 25\ m$$
The radius of a circle whose area is equal to the sum of the areas of two circles of radii are 5 cm and 12 cm is
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13 cm
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14 cm
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15 cm
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none
Explanation
Given two circle radii are $$5 cm$$ and $$12 cm$$
Then,
Area of circle of radius 5 cm $$=$$$$\pi r^{2}=\pi (5)^{2}=25\pi $$ sq cm
Area of circle of radius 12 cm $$=$$$$\pi r^{2}=\pi (12)^{2}=144\pi $$sq cm
So area of circle whose area is equal to sum of areas of two circles$$=$$$$25\pi +144\pi =169\pi $$ sq cm
Let the radius of the bigger circle be $$=$$R cm
$$\therefore \pi R^{2}=169\pi$$
$$\Rightarrow R^{2}=169$$
$$\Rightarrow R=13 cm$$
Find the perimeter of a circle whose radius is 7 cm (in cm)
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$$\displaystyle 12\pi $$
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$$\displaystyle 14\pi $$
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$$\displaystyle 16\pi $$
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$$\displaystyle 10\pi $$
Explanation
Perimeter of a circle $$ = 2\pi r $$, where r is the radius of the circle
So, perimeter of the given circle $$ = 2 \times \pi \times 7 = 14 \pi $$
If the area of the circle be $$ \displaystyle 154 \text{ cm}^{2},$$ then its radius is equal to:
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$$12\text{ cm}$$
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$$8\text{ cm}$$
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$$7\text{ cm}$$
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None of these
Explanation
Area of the circle $$=154\displaystyle \text{ cm}^{2}$$
$$\because $$ Area $$=\displaystyle \pi r^{2}$$
$$\therefore \pi r^2=154$$
$$\Rightarrow$$ $$\displaystyle r^{2}=\frac{154\times 7}{22}$$
$$ \Rightarrow r^2 = \displaystyle 7\times 7$$
$$\displaystyle \Rightarrow r=7\text{ cm}$$
If the circumference of a circle be $$8.8 \text{ m}$$ then its radius is equal to -
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$$1.60 \text{ m}$$ (approx)
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$$1.61 \text{ m}$$ (approx)
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$$1.40 \text{ m}$$ (approx)
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None of these
Explanation
Circumference of a circle, $$\displaystyle C=2\pi r $$
or $$\displaystyle r=\frac{C}{2\pi } $$
$$=\displaystyle \frac{8.8\times 7}{2\times 22} $$ $$= 1.4 \text{ m}$$
If the radius of a circle be $$r$$ $$ cm$$, then its area will be equal to-
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$$ \displaystyle 2\pi r^{2}cm^{2} $$
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$$ \displaystyle \pi r^{2}cm^2 $$
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$$ \displaystyle 2\pi rcm^{2} $$
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None of these
Explanation
If radius is $$r $$ $$cm$$, then
$$area=\pi r^2\,\, cm^2 $$.
Option B is correct.
What is the circumference of a circle whose radius is 8 cm?
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$$ \displaystyle 8 \pi $$
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$$ \displaystyle 16\pi $$
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$$ \displaystyle 61 \pi $$
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$$ \displaystyle 24 \pi $$
Explanation
Circumference=$$\displaystyle 2\pi r$$
=$$\displaystyle 2\times \pi \times 8$$
=16$$\displaystyle \pi $$ cm
The radius of a circle is increased by $$5$$ units. What is ratio of the new circumference and the new diameter?
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$$x-5$$
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$$\pi +5$$
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$$\pi$$
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$$\pi -1$$
Explanation
Let the radius of the circle be $$r$$.
$$\therefore$$ New circumference $$=2\pi(r+5)$$
and new diameter $$=2(r+5)$$
$$\therefore$$ Ratio$$=\cfrac{2\pi(r+5)}{2(r+5)}$$
$$=\pi$$
If circumference of a circle is $$\displaystyle 3\pi $$, then its area is
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$$\displaystyle \frac{7\pi }{2}$$
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$$\displaystyle 9\pi ^{2}$$
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$$\displaystyle 4\pi ^{2}$$
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$$\displaystyle \frac{9\pi }{4}$$
Explanation
$$\Rightarrow$$ Circumference of a circle $$=3\pi$$
$$\Rightarrow$$ $$2\pi r=3\pi$$
$$\Rightarrow$$ $$2r=3$$
$$\Rightarrow$$ $$r=\dfrac{3}{2}$$
$$\Rightarrow$$ Area of a circle $$=\pi r^2$$
$$=\pi\times \left(\dfrac{3}{2}\right)^2$$
$$=\dfrac{9}{4}\pi$$
$$ \displaystyle \frac{1}{5}\, of\,10 km= $$ _____m
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2
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200
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20
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2000
Explanation
$$ \displaystyle \frac{1}{5} $$ of 10 km
$$ \displaystyle \frac{1}{5}\times10 \ km $$
= 2 km=2000 m
A wall is made up of square bricks of unit length. Then its area is _____
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1 sq unit
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3 sq units
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20 sq units
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24 sq units
Explanation
As 24 square bricks are required for the wall
So Area = 24 $$ \times $$ area of one brick =$$ 24 \times 1$$= 24 sq units
A figure is formed by putting two squares one on the other as shown below. If the length of each side of the two squares is $$8$$ cm, then the perimeter of the formed figure is
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$$56$$ cm
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$$64$$ cm
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$$32$$ cm
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$$48$$ cm
Explanation
New dimensions are $$b = 16$$ & $$ l=8 $$
$$\displaystyle \therefore $$Perimeter of the figure formed
$$\displaystyle = 16+8+16+8= \displaystyle 48$$ cm
The total boundary length of circle is called
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area
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volume
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circumference
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diameter
Explanation
Boundary length of circle is called circumference which is the same as perimeter of circle.
Area of a rectangle is $$120 $$ $$m^2$$ and the breadth is $$5 m$$ . Then its length is
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$$204 m$$
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$$24 m$$
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$$28 m$$
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$$26 m$$
Explanation
We know, a
rea of rectangle = $$ l \times b $$
Since, area $$= 120$$
$$\therefore $$ $$l \times b = 120$$
$$\Rightarrow $$ length =$$l =\displaystyle \frac{120}{5}=24 m$$
Circumference of a circle is equal to
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$$\displaystyle \pi r$$
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$$2\displaystyle \pi r$$
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$$\displaystyle \frac{\pi r}{2}$$
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$$\displaystyle 2+\frac{\pi r}{2}r$$
Explanation
The circumference of a circle whose radius is equal to $$r$$ is given by $$2\pi r.$$
The circumference of a circle is called
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chord
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segment
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boundary
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None
Explanation
Perimeter of circle = Circumference ---eq.1
Perimeter = Boundary ---eq.2
from eq.1 & eq.2
Circumference = Boundary
$$ \therefore $$ The circumference of a circle is called boundary.
If the radius of a circle is $$\dfrac{7}{\sqrt{\pi}}$$, what is the area of the circle (in $$cm^2$$)?
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$$154$$
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$$\dfrac{49}{\pi}$$
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$$22$$
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$$49$$
Explanation
Given: Radius of circle $$(r)=\dfrac{7}{\sqrt{\pi}}$$
Area of the circle $$=\pi (r)^2$$
$$=\pi\times (\dfrac{7}{\sqrt{\pi}})^2$$
$$=\pi\times \dfrac{49}{\pi}$$
$$=49 cm^2$$
Find the area of the triangle shown in figure.
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$$20$$
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$$30$$
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$$35$$
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$$40$$
Explanation
We know, area of a triangle $$A=\dfrac{1}{2}\times b\times h$$,
where
$$b$$
is the length of the base and $$h$$
is the height.
In the figure, the base of the right-angled triangle is 8 and the height is 5.
$$\therefore$$ Area $$=\dfrac{1}{2}\times 8\times 5$$
$$=20$$
The ______ of a circle is called the circumference.
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area
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volume
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perimeter
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radius
Explanation
The perimeter of a circle is called the circumference.
Since, the circumference of a circle is the distance across the boundary of the circle.
The distance, once around the circle is called
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diameter
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center
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circumference
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chord
Explanation
The distance around the circle is called circumference.
Example:
The circumference of the circle is the boundary of t he
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perimeter
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radius
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diameter
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circle
Explanation
The circumference of the circle is the distance around by the circle.
The circumference of the circle is calculated by the formula
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$$4\pi r$$
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$$2\pi r^2$$
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$$3\pi r$$
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none of these
Explanation
The circumference of the circle is calculated by the formula $$2\pi r$$, where $$r$$ is radius of the circle.
The dotted line represents the
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center
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diameter
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circumference
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chord
Explanation
As the circumference of a circle is the distance around by the circle,
the dotted line represents the circumference.
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