Question

From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed (as shown in the adjoining figure) find the area of the remaining sheet.

pls explain the answer with proper steps and statements. ​

Answer 1

Step-by-step explanation:

Given:

Radius of the circular card sheet = 14 cm

Radius of two small circles = 3.5cm

Length of the rectangle inside it = 3cm

Breadth of the rectangle inside it = 1cm

To find:

Area of the remaining sheet.

First, we will find the area of the whole circle =

πr^2

$\frac{22}{7} \times 14 \times 14 = area$

(cancellation)

$616 {cm}^{2} = area \: of \: the \: whole \: circle$

Second step-

Now we will find the area of 2 small circles.

$3.14 \times 3.5 \times 3.5 \times 2 = area$

$76.93 \: {cm}^{2} = area$

Third step-

Now we will find the area of the rectangle.

$l \times b = area$

$3 \times 1 = area$

$3 {cm}^{2}$

Total area= 76.93+3 = 79.93 cm^2

Area of the remaining sheet =

616- 79.93 = 536.07 cm^2

: Area of the remaiming sheet is 536.07 cm^2....

Answer 2

Answer:

The area of remaining sheet is 536 cm².

Step-by-step explanation:

$\star\:{\underline{\boxed{\rm{\pink{Given : - }}}}}$

• ✧ Radius of circular sheet = 14cm
• ✧ Radius of Small circle = 3.5cm
• ✧ Length of Rectangle = 3cm
• ✧ Breadth of Rectangle = 1cm

$\begin{gathered}\end{gathered}$

$\star\:{\underline{\boxed{\rm{\purple{To \: Find : - }}}}}$

• ✧ Area of Circular card
• ✧ Area of 2 small circles
• ✧ Area of Rectangle
• ✧ Area of Remaining sheet

$\begin{gathered}\end{gathered}$

$\star\:{\underline{\boxed{\rm{\blue{Solution : - }}}}}$

Finding area of circular sheet by substituting the values in the formula :

• ✧ Radius = 14 cm.
• ✧ π = 22/7

${\implies{\sf{Area_{(Circular Sheet)} = \pi{R}^{2}}}}$

${\implies{\sf{Area_{(Circular Sheet)} = \dfrac{22}{7} \times {(14)}^{2}}}}$

${\implies{\sf{Area_{(Circular Sheet)} = \dfrac{22}{7} \times {(14 \times 14)}}}}$

${\implies{\sf{Area_{(Circular Sheet)} = \dfrac{22}{\cancel{7}} \times {( \cancel{14} \times 14)}}}}$

${\implies{\sf{Area_{(Circular Sheet)} = {22}\times {(2 \times 14)}}}}$

${\implies{\sf{Area_{(Circular Sheet)} = {22}\times {(28)}}}}$

${\implies{\sf{Area_{(Circular Sheet)} = {22}\times 28}}}$

${\implies{\sf{\underline{\underline{\red{Area_{(Circular Sheet)} = 616 \: {cm}^{2}}}}}}}$

Hence, the area of circular sheet is 616 cm².

$\rule{300}{1.5}$

Finding the area of 2 small circles by substituting the values in the formula :

• ✧ Radius = 3.5 cm
• ✧ π = 22/7

$\implies{\sf{Area_{(Small \: Circles)} = 2 \times \pi{r}^{2}}}$

${\implies{\sf{Area_{(Small \: Circles)} = 2 \times \dfrac{22}{7} \times {(3.5)}^{2}}}}$

${\implies{\sf{Area_{(Small \: Circles)} = 2\times \dfrac{22}{7} \times { \bigg( \dfrac{35}{10} \bigg)}^{2}}}}$

${\implies{\sf{Area_{(Small \: Circles)} = 2 \times \dfrac{22}{7} \times { \bigg( \cancel{\dfrac{35}{10}} \bigg)}^{2}}}}$

${\implies{\sf{Area_{(Small \: Circles)} = 2 \times \dfrac{22}{7} \times { \bigg( \dfrac{7}{2} \bigg)}^{2}}}}$

${\implies{\sf{Area_{(Small \: Circles)} = 2 \times \dfrac{22}{7} \times { \bigg( \dfrac{7}{2} \times \dfrac{7}{2} \bigg)}}}}$

${\implies{\sf{Area_{(Small \: Circles)} = 2 \times \dfrac{\cancel{22}}{\cancel{7}} \times { \bigg( \dfrac{\cancel{7}}{\cancel{2}} \times \dfrac{7}{2} \bigg)}}}}$

${\implies{\sf{Area_{(Small \: Circles)} = 2 \times 11 \times \dfrac{7}{2}}}}$

${\implies{\sf{Area_{(Small \: Circles)} = 22\times \dfrac{7}{2}}}}$

${\implies{\sf{Area_{(Small \: Circles)} = \cancel{22}\times \dfrac{7}{\cancel{2}}}}}$

${\implies{\sf{Area_{(Small \: Circles)} = 11 \times 7}}}$

${\implies{\sf{\underline{\underline{\red{Area_{(Small \: Circles)} =77 \: {cm}^{2}}}}}}}$

Area of 2 small circles is 77 cm².

$\rule{300}{1.5}$

Finding the area of rectangle by substituting the values in the formula :

• ✧ Lenght of rectangle = 3 cm.
• ✧ Breadth of Rectangle = 1 cm.

${\implies\sf{Area_{(Rectangle)} = lb}}$

${\implies\sf{Area_{(Rectangle)} = l \times b}}$

${\implies\sf{Area_{(Rectangle)} = 3 \times 1}}$

${\implies{\sf{\underline{\underline{\red{Area_{(Rectangle)} = 3 \: {cm}^{2}}}}}}}$

Hence, the area of rectangle 3 cm².

$\rule{300}{1.5}$

Now, finding the area of remaining sheet :

• ✧ Area of circular sheet = 616 cm².
• ✧ Area of 2 small circles = 77 cm²
• ✧ Area of rectangle = 3 cm².

${\implies{\small{\sf{Area_{(Remaining Sheet)}= Area_{(Circular \: Sheet)} - Area_{(Small \: Circles)} - Area_{(Rectangle)}}}}}$

${\implies{\sf{Area_{(Remaining Sheet)}= 616 - 77 - 3}}}$

${\implies{\sf{Area_{(Remaining Sheet)}= 616 - 77 + 3}}}$

${\implies{\sf{Area_{(Remaining Sheet)}= 616 -80}}}$

${\implies{\sf{\underline{\underline{\red{Area_{(Remaining Sheet)}= 536 \: {cm}^{2}}}}}}}$

Hence, the area of sheet is 536 cm².

$\begin{gathered}\end{gathered}$

$\star \: {\underline{\boxed{\rm{\green{Learn \: More: - }}}}}$

Circle :

• ✧ A circle is a round shaped figure that has no corners or edges. 
• ✧ In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Formula related to circle :

• ✧ Area of circle = πr²
• ✧ Diameter of circle = 2×r
• ✧ Circumference of circle = 2πr

$\underline{\rule{220pt}{3.5pt}}$