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

Fact: circumference of a circle whose radius is \$r\$ is given by \$2\pi r\$Here \$r=7\$ cm Hence circumference of the circle \$=2\pi (7)=2\cdot \dfrac{22}{7}\cdot 7=2\cdot 22=44\$ cm

Q: Find the area of a quadrant of a circle whose radius is \$14\$ cm.

Given the radius of the circle is \$14\$ cm.Then the area of the circle \$=\pi r^2=\dfrac{22}{7}\times (14)^2=\dfrac{22}{7}\times 4\times 7^2=4\times 154\$ cm\$^2\$.Then the area of a quadrant of the circle is \$\dfrac{4\times 154}{4}=154\$ cm\$^2\$.

Q: If the diameter of a semi circular protractor is 14 cm, then find its perimeter .

Perimeter if semicircle \$=\pi r + 2r\$since \$d=14cm\$\$r=\dfrac{d}{2} = \dfrac{{14}}{2} = 7cm\$\$\dfrac{d}{2} = \dfrac{{14}}{2} = 7cm\$\$ = 22cm + 14cm\$\$ = 36cm.\$

Q: If the circumference of a circular sheet is \$154\ m,\$ find its radius. Also find the area of the sheet. \$\bigg(\$Take \$\pi=\dfrac{22}{7}\bigg)\$

Circumference of the circular sheet\$=154\$m\$\Rightarrow 2\pi r=154\$m\$\Rightarrow r=\dfrac{154}{2\pi}\$\$\Rightarrow r=\dfrac{154\times 7}{2\times 22}=24.5\$mNow, Area of circular sheet\$=\pi r^2=\dfrac{22}{7}\times 24.5\times 24.5\$\$=22\times 3.5\times 24.5=1886.5m^2\$.Thus, the radius and area of circular sheet are \$24.5\$m and \$1886.5m^2\$ respectively.

Q: A path \$5 \ cm\$ wide runs along inside a square park of side \$100 \ cm\$. Find the area of the path . Also find the cost of cementing at the the rate of Rs \$250\$ per \$10 \ sq. cm\$.

Given inner side of square park, \$s = 100 \ cm\$ Area of inner square \$={100}^{2}= 10000 \ cm^2\$width of path,\$ w = 5 \ cm\$Outer side of square \$= 100 + 5+5 = 110 \ cm\$ Area of outer square \$= {110}^{2} = 12100 \ cm^2\$ Area of path \$= 12100 - 10000 = 2100 \ cm^2\$Cost of cementing at the rate of Rs \$250\$ per \$10\$ sq cm \$=\$ Rs \$250 \times 210=\$ Rs \$52500\$\$\therefore \$ Cost of cementing a \$2100 \ cm^2\$ path \$=Rs. \ 52500\$

Q: A floor is 5 m long and 4 m wide. A square carpet of sides 3 m is laid on the floor. Find the area of the floor that is not carpeted.

Given :Length of the floor is \$5m\$The breadth of the floor is \$4m\$So, ( applying ar. \$l \times b\$ )ar. of floor \$=4m\times 5m=20m^2.\$ Side of the carpet is \$3m\$So, (applying ar. of sq. \$= side × side (s) )\$area of carpet\$=3m\times3m=9m^2.\$ To find the area of the floor that is not carpeted or (uncarpeted) we will \$(-)\$ minus the ar. of the floor from ar. of carpet area which is not carpeted or( uncarpeted ) \$=20m^2-9m^2\$\$=11m^2.\$ Hence, answer Is \$11m^2.\$

Q: From the circular sheet of radius \$4\ cm\$, a circle of radius \$3\ cm\$ is removed. Find the area of the remaining sheet. \$(Take\ \pi=3.14)\$

The area of the circular sheet with \$4\;{\rm{cm}}\$ radius is, \$A = \pi {r^2}\$ \$ = 16\pi \$ The area of the circular sheet with \$3\;{\rm{cm}}\$ radius is, \$A = \pi {r^2}\$ \$ = 9\pi \$ Since the circle with radius \$3\;{\rm{cm}}\$ is removed, then the remaining area is, \$A = 16\pi - 9\pi \$ \$ = 7\pi \$ \$ = 7 \times 3.14\$ \$ = 21.98\;{\rm{c}}{{\rm{m}}^2}\$

Q: Find the area of a circle whose radius is \$21\,cm.\$

Given, radius \$r = 21 \,cm\$ and \$\pi = \dfrac{22}{7}\$Then,Area of the circle = \$\pi r^2\$ sq units\$= \dfrac{22}{7} \times 21 \times 21\$\$= 22 \times 3 \times 21\$\$= 1386 \,cm^2\$

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

circumference of the circle with radius \$r\$ is =\$ 2\pi r\$\$\Rightarrow 2\pi r=14\Rightarrow r=\dfrac{14}{2\pi }=\dfrac{14\times 7}{2\times 22}=\dfrac{49}{22}\$ \$\Rightarrow r =2.227\ cm\$

Q: What is the area of the circle that can be inscribed in a square of side 6cm?

From figure, \$AB=BC=CD=DA=6\ cm\$\$PR\$ is the diameter of the circle, inscribed in the square \$ABCD\$\$\therefore PR=side \ of \ the \ square=6\ cm\$\$\therefore Radius=\dfrac{6}{2}=3\$\$Area=\pi r^2=\dfrac{22}{7}\times 3^2\$\$=\dfrac{22}{7}\times 9\$\$\therefore Area \ of \ circle=28.28\ cm^2\$

Question 1

Find the circumference of a circle whose radius is $7$cm.

Accepted Answer

Fact:  circumference of a circle whose radius is $r$ is given by $2\pi r$Here $r=7$ cm Hence circumference of the circle $=2\pi (7)=2\cdot \dfrac{22}{7}\cdot 7=2\cdot 22=44$ cm

Question 2

Find the area of a quadrant of a circle whose radius is $14$ cm.

Accepted Answer

Given the radius of the circle is $14$ cm.Then the area of the circle $=\pi r^2=\dfrac{22}{7}\times (14)^2=\dfrac{22}{7}\times 4\times 7^2=4\times 154$ cm$^2$.Then the area of a quadrant of the circle is $\dfrac{4\times 154}{4}=154$ cm$^2$.

Question 3

If the diameter of a semi circular protractor is 14 cm, then find its perimeter .

Accepted Answer

Perimeter if semicircle $=\pi r + 2r$since $d=14cm$$r=\dfrac{d}{2} = \dfrac{{14}}{2} = 7cm$$\dfrac{d}{2} = \dfrac{{14}}{2} = 7cm$$ = 22cm + 14cm$$ = 36cm.$

Question 4

If the circumference of a circular sheet is $154\ m,$ find its radius. Also find the area of the sheet. $\bigg($Take $\pi=\dfrac{22}{7}\bigg)$

Accepted Answer

Circumference of the circular sheet$=154$m$\Rightarrow 2\pi r=154$m$\Rightarrow r=\dfrac{154}{2\pi}$$\Rightarrow r=\dfrac{154\times 7}{2\times 22}=24.5$mNow, Area of circular sheet$=\pi r^2=\dfrac{22}{7}\times 24.5\times 24.5$$=22\times 3.5\times 24.5=1886.5m^2$.Thus, the radius and area of circular sheet are $24.5$m and $1886.5m^2$ respectively.

Question 5

A path $5 \ cm$ wide runs along inside a square park of side $100 \ cm$. Find the area of the path . Also find the cost of cementing at the the rate of Rs $250$ per $10  \ sq. cm$.

Accepted Answer

Given inner side of square park, $s = 100 \ cm$ Area of inner square $={100}^{2}= 10000 \ cm^2$width of path,$ w = 5 \ cm$Outer side of square $= 100 + 5+5 = 110 \ cm$ Area of outer square $= {110}^{2} = 12100 \ cm^2$ Area of path $= 12100 - 10000 = 2100 \ cm^2$Cost of cementing at the rate of Rs $250$ per $10$ sq cm $=$ Rs $250 \times 210=$ Rs $52500$$\therefore $ Cost of cementing a $2100 \ cm^2$ path $=Rs. \ 52500$

Question 6

A floor is 5 m long and 4 m wide. A square carpet of sides 3 m is laid on the floor. Find the area of the floor that is not carpeted.

Accepted Answer

Given :Length of the floor is $5m$The breadth of the floor is $4m$So, ( applying ar. $l \times b$ )ar. of floor $=4m\times 5m=20m^2.$ Side of the carpet is $3m$So, (applying ar. of sq. $= side &#215; side (s) )$area of carpet$=3m\times3m=9m^2.$ To find the area of the floor that is not carpeted or (uncarpeted) we will $(-)$ minus the ar. of the floor from ar. of carpet area which is not carpeted or( uncarpeted ) $=20m^2-9m^2$$=11m^2.$ Hence, answer Is $11m^2.$

Question 7

From the circular sheet of radius $4\ cm$, a circle of radius $3\ cm$  is removed. Find the area of the remaining sheet.  $(Take\  \pi=3.14)$

Accepted Answer

The area of the circular sheet with $4\;{\rm{cm}}$ radius is,&#10;&#10;$A = \pi {r^2}$&#10;&#10;$ = 16\pi $&#10;&#10;The area of the circular sheet with $3\;{\rm{cm}}$ radius is,&#10;&#10;$A = \pi {r^2}$&#10;&#10;$ = 9\pi $&#10;&#10;Since the circle with radius $3\;{\rm{cm}}$ is removed, then the&#10;remaining area is,&#10;&#10;$A = 16\pi  - 9\pi $&#10;&#10;$ = 7\pi $&#10;&#10;$ = 7 \times 3.14$&#10;&#10;$ = 21.98\;{\rm{c}}{{\rm{m}}^2}$

Question 8

Find the area of a circle whose radius is $21\,cm.$

Accepted Answer

Given, radius $r = 21 \,cm$ and $\pi = \dfrac{22}{7}$Then,Area of the circle = $\pi r^2$ sq units$= \dfrac{22}{7} \times 21 \times 21$$= 22 \times 3 \times 21$$= 1386 \,cm^2$

Question 9

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

Accepted Answer

circumference of the circle with radius $r$ is =$ 2\pi r$$\Rightarrow 2\pi r=14\Rightarrow r=\dfrac{14}{2\pi }=\dfrac{14\times 7}{2\times 22}=\dfrac{49}{22}$ $\Rightarrow r =2.227\ cm$

Question 10

What is the area of the circle that can be inscribed in a square of side 6cm?

Accepted Answer

From figure, $AB=BC=CD=DA=6\ cm$$PR$ is the diameter of the circle, inscribed in the square $ABCD$$\therefore PR=side \ of \ the \ square=6\ cm$$\therefore Radius=\dfrac{6}{2}=3$$Area=\pi r^2=\dfrac{22}{7}\times 3^2$$=\dfrac{22}{7}\times 9$$\therefore Area \ of \ circle=28.28\ cm^2$