2 Marks Questions

Question 12 Marks

Find the radius of a circle whose circumference is: $6.6\ km.$

Answer

Let the radius of the circle be $r\ km.$ Circumference of the circle $(C) =6.6\text{km}$
$\Rightarrow2\times\frac{22}{7}\times\text{r}=6.6$
$\Rightarrow\text{r}=\frac{6.6\times7}{2\times22}=1.05\text{km}$

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Question 22 Marks

Find the area of a circle whose radius is:
$2.1\ m.$

Answer

We know that the area $A$ of a circle of radius $r$ is given by $A =\pi\text{r}^2$
Here, $r =2.1\text{m}$
$\therefore\text{A}=\frac{22}{7}\times\text{2.1}^2=13.86\text{m}^2$

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Question 32 Marks

A water sprinkler in a lawn sprays water as far as $7m$ in all directions. Find the length of the outer edge of wet grass.

Answer

The wet grass forms a circular region of radius $7m.$
$\therefore$ The length of the outer edge of the wet grass is $2\pi\text{}r=\Big(2\times\frac{22}{7}\times7\Big)\text{m}=44\text{m}.$

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Question 42 Marks

Find the circumference of a circle whose diameter is:$7\ cm.$

Answer

We know that the circumference of a circle of radius $r$ is given by $C =2\pi\text{r}$
Here, $d = 7\ cm$
Then, $r = 1 = 3.5\ cm$
$\Rightarrow\text{C}=2\times\frac{22}{7}\times3.5=22\text{cm}$

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Question 52 Marks

Find the area of a circle whose diameter is: $5.6\ m.$

Answer

Let $r$ be the radius of the circle.
Then,$ r =\frac{5.6}{2}=2.8\text{m}.$
$\therefore$ Area of the circle $=\pi\text{r}^2$
$=\text{A}=\frac{22}{7}\times2.8^2\text{m}^2$
$=\text{A}=24.64\text{m}^2$

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Question 62 Marks

Find the radius of a circle whose circumference is: $42\ cm.$

Answer

Let the radius of the circle be $r\ cm.$
Circumference of the circle $(C) =42\text{cm}$
$\Rightarrow2\times\frac{22}{7}\times\text{r}=42$
$\Rightarrow\text{r}=\frac{42\times7}{2\times22}=6.68\text{cm}$

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Question 72 Marks

Find the radius of a circle whose circumference is:
$52.8\ cm.$

Answer

Let the radius of the circle be $r\ cm.$
Circumference of the circle $(C) =52.8\text{cm}$
$\Rightarrow2\times\frac{22}{7}\times\text{r}=52.8$
$\Rightarrow\text{r}=\frac{52.8\times7}{2\times22}=8.4\text{cm}$

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Question 82 Marks

Find the diameter of a circle whose circumference is: $88\ m.$

Answer

Let the radius of the circle be $r\ m.$
Circumference of the circle $ (C) =88\text{m}$
$\Rightarrow2\times\frac{22}{7}\times\text{r}=88$
$\Rightarrow\text{r}=\frac{88\times7}{2\times22}=14\text{m}$
Now, diameter $=2\times\text{r}=2\times14=28\text{m}$

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Question 92 Marks

Find the area of a circle whose diameter is: $7\ km.$

Answer

Let $r$ be the radius of the circle.
Then,$ r =\frac{7}{2}=3.5\text{km}.$
$\therefore$ Area of the circle $=\pi\text{r}^2$
$=\text{A}=\frac{22}{7}\times3.5^2\text{km}^2$
$=\text{A}=38.5\text{km}^2$

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Question 102 Marks

A horse is tied to a pole with $28\ m$ long string. Find the area where the horse can graze. $\Big(\text{Take }\pi=\frac{22}{7}\Big).$

Answer

We have: Length of the string $= 28\ m$
The area over which the horse can graze is the same as the area of a circle of radius $28\ m.$
Hence, required area $=\pi\text{r}^2=\frac{22}{7}\times28\times28=22\times4\times28=2464\text{m}^2.$

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Question 112 Marks

Find the circumference of a circle whose radius is: $14\ cm.$

Answer

We know that the circumference of a circle of radius $r$ is given by $\text{C}=2\pi\text{r}$
Here, $r = 14\ cm$
$\Rightarrow\text{C}=2\times\frac{22}{7}\times14=88\text{cm}.$

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Question 122 Marks

Find the diameter of a circle whose circumference is:
$11.0\ km.$

Answer

Let the radius of the circle be $r\ km.$
Circumference of the circle $(C) =11.0\text{km}$
$\Rightarrow2\times\frac{22}{7}\times\text{r}=11$
$\Rightarrow\text{r}=\frac{11\times7}{2\times22}=1.75\text{km}$
Now, diameter $=2\times\text{r}=2\times1.75=3.5\text{km}$

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Question 132 Marks

Find the diameter of a circle whose circumference is: $12.56\ cm$

Answer

Let the radius of the circle be $r\ cm.$
Circumference of the circle $(C) =12.56\text{cm}$
$\Rightarrow2\times\frac{22}{7}\times\text{r}=12.56$
$\Rightarrow\text{r}=\frac{12.56\times7}{2\times22}=1.99\text{cm}$
Now, diameter $=2\times\text{r}=2\times1.99=3.99\text{cm}$

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Question 142 Marks

Find the circumference of a circle whose radius is: $4\ km.$

Answer

We know that the circumference of a circle of radius $r$ is given by $C =2\pi\text{r}$
Here, $r = 4\ km$
$\Rightarrow\text{C}=2\times\frac{22}{7}\times4=25.142\text{km}$

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Question 152 Marks

Find the area of a circle whose radius is: $7\ cm.$

Answer

We know that the area $A$ of a circle of radius $r$ is given by $A =\pi\text{r}^2$
Here, r $=7\text{cm}$
$\therefore\text{A}=\frac{22}{7}\times\text{7}^2=154\text{cm}^2$

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Question 162 Marks

The moon is about $384400\ km$ from the earth and its path around the earth is nearly circular. Find the circumference of the path described by the moon in lunar month.

Answer

We have: The radius of the path described by the moon around the earth $= 384400\text{km}$
$\therefore$ The circumference of the path described by the moon $C =2\pi\text{r}=2\times\Big(\frac{22}{7}\times384400\Big)\text{km}=2416228.57\text{km}$

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Question 172 Marks

Find the circumference of a circle whose radius is: $10m.$

Answer

We know that the circumference of a circle of radius $r$ is given by $C =2\pi\text{r}$
Here, $r = 14\ cm$
$\Rightarrow\text{C}=2\times\frac{22}{7}\times10=62.86\text{m}$

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Question 182 Marks

Find the area of a circle whose radius is: $7\ km.$

Answer

We know that the area $A$ of a circle of radius $r$ is given by $A =\pi\text{r}^2$
Here, $r =7\text{km}$
$\therefore\text{A}=\frac{22}{7}\times\text{7}^2=154\text{km}^2$

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Question 192 Marks

Find the circumference of a circle whose diameter is: $11.2\ km.$

Answer

We know that the circumference of a circle of radius $r$ is given by $C =2\pi\text{r}$
Here, $d =11.2\text{km}$
Then, $ r =\frac{11.2}{2}=5.6\text{km}$
$\Rightarrow\text{C}=2\times\frac{22}{7}\times5.6=35.2\text{km}$

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Question 202 Marks

Find the circumference of a circle whose diameter is: $4.2\ cm.$

Answer

We know that the circumference of a circle of radius $r$ is given by $C =2\pi\text{r}$
Here, $ d =4.2\text{cm}$
Then, $r =\frac{4.2}{2}=2.1\text{cm}$
$\Rightarrow\text{C}=2\times\frac{22}{7}\times2.1=13.2\text{cm}$

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Question 212 Marks

Find the area of a circle whose diameter is: $8.4\ cm.$

Answer

Let $r$ be the radius of the circle. Then,$ r =\frac{8.4}{2}=4.2\text{cm}$
$\therefore$ Area of the circle $=\pi\text{r}^2$
$=\text{A}=\frac{22}{7}\times4.2^2\text{cm}^2$
$=\text{A}=55.44\text{cm}^2$

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