From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. Take $\left( {\pi = 3.14} \right)$
Answer
363.3k+ views
Hint – In this question from the main circular sheet of radius 4 cm, a smaller circle of radius 3 cm is removed. So using the basic formula for area of circle, we can easily remove the smaller circular area from the larger circular area. This concept will give us the required remaining area.
Complete step-by-step answer:
Area of the circle of radius r is given as ${\text{A = }}\pi {r^2}$……………………. (1)
Now the radius of the larger circle centered at O2 is having radius r1=4cm……………. (2)
The radius of the smaller circle that is being removed from the larger circle is centered at O1 and has the radius r2=3cm……………………. (3)
Now putting the values in equation (1)
Area of larger circle centered at 02,
${{\text{A}}_2} = \pi {\left( 4 \right)^2} = 16\pi {\text{c}}{{\text{m}}^2}$…………………………… (4)
Now putting the values in equation (1) again
The area of smaller circle centered at O1,
${{\text{A}}_1} = \pi {\left( 3 \right)^2} = 9\pi {\text{c}}{{\text{m}}^2}$……………………… (5)
Now the required remaining area which is shaded in diagram is equal to the difference of larger circle centered at 02 and the area of smaller circle centered at O1.
Thus using equation (4) and (5) we can say that
$
{\text{Area req = 16}}\pi {\text{ - 9}}\pi \\
\Rightarrow 7\pi \\
$
Using $\pi = 3.14$ we get
Area required = $7 \times 3.14 = 21.98{\text{c}}{{\text{m}}^2}$
Note – Whenever we face such types of problems the key concept is to think of the diagrammatic representation using the data provided in the problem. This will give you the actual understanding about which area has to be removed from which area in order to reach the required area.
Complete step-by-step answer:

Area of the circle of radius r is given as ${\text{A = }}\pi {r^2}$……………………. (1)
Now the radius of the larger circle centered at O2 is having radius r1=4cm……………. (2)
The radius of the smaller circle that is being removed from the larger circle is centered at O1 and has the radius r2=3cm……………………. (3)
Now putting the values in equation (1)
Area of larger circle centered at 02,
${{\text{A}}_2} = \pi {\left( 4 \right)^2} = 16\pi {\text{c}}{{\text{m}}^2}$…………………………… (4)
Now putting the values in equation (1) again
The area of smaller circle centered at O1,
${{\text{A}}_1} = \pi {\left( 3 \right)^2} = 9\pi {\text{c}}{{\text{m}}^2}$……………………… (5)
Now the required remaining area which is shaded in diagram is equal to the difference of larger circle centered at 02 and the area of smaller circle centered at O1.
Thus using equation (4) and (5) we can say that
$
{\text{Area req = 16}}\pi {\text{ - 9}}\pi \\
\Rightarrow 7\pi \\
$
Using $\pi = 3.14$ we get
Area required = $7 \times 3.14 = 21.98{\text{c}}{{\text{m}}^2}$
Note – Whenever we face such types of problems the key concept is to think of the diagrammatic representation using the data provided in the problem. This will give you the actual understanding about which area has to be removed from which area in order to reach the required area.
Last updated date: 01st Oct 2023
•
Total views: 363.3k
•
Views today: 4.63k
Recently Updated Pages
What do you mean by public facilities

Slogan on Noise Pollution

Paragraph on Friendship

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

What is the Full Form of ILO, UNICEF and UNESCO

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Why are resources distributed unequally over the e class 7 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Briefly mention the contribution of TH Morgan in g class 12 biology CBSE

What is the past tense of read class 10 english CBSE
