areas related to circles - areas of combinations of plane figures (class 10 maths)
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Areas related to circles - Areas of combinations of plane figures (Class 10 Maths). Let's tute is an E-school or E- platform which is free for the student.Students will watch "MATHS" Videos for conceptual understanding. Contact Us - Website - www.letstute.com YouTube - www.youtube.com/letstuteTRANSCRIPT
Areas Related To Circles
Problems based onAreas of combinations of plane figures
Chapter : Areas Related To Circles Website: www.letstute.com
Chapter : Areas Related To Circles Website: www.letstute.com
Q) From each corner of a square of side 8 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in the figure. Find the area of the remaining portion of the square.
Given: Side of the square = 8 cm Quadrant of radius = 1 cm
To Find: Area of the remaining = ? portion of the square
Diameter of circle = 2 cm
Problems based onAreas of combinations of plane figures
Chapter : Areas Related To Circles Website: www.letstute.com
Solution: Area of square ABCD
=
Problems based onAreas of combinations of plane figures
= 8 x 8 cm2
= 64 cm2
Area of a quadrant of radius 1 cm
=
=
=
[∵ 900
3600= 14 ]
=
Chapter : Areas Related To Circles Website: www.letstute.com
=
Problems based onAreas of combinations of plane figures
Area of four quadrants of radius 1 cm
=
=
= 4 x area of 1 quadrant
=
Chapter : Areas Related To Circles Website: www.letstute.com
Area of circle of diameter 2 cm
¿𝛑 𝐫𝟐¿ [𝟐𝟐𝟕 ×𝟏×𝟏]𝐜𝐦𝟐
¿ [𝟐𝟐𝟕 ]𝐜𝐦𝟐
Problems based onAreas of combinations of plane figures
[
Chapter : Areas Related To Circles Website: www.letstute.com
Area of the remaining portion of square ABCD
¿¿ [𝟔𝟒−𝟐𝟐𝟕 −
𝟐𝟐𝟕 ]𝐜𝐦𝟐
Problems based onAreas of combinations of plane figures
¿ [𝟒𝟒𝟖−𝟐𝟐−𝟐𝟐𝟕 ]𝐜𝐦𝟐
¿ [𝟒𝟒𝟖−𝟒𝟒𝟕 ]𝐜𝐦𝟐
Chapter : Areas Related To Circles Website: www.letstute.com
¿𝟒𝟎𝟒𝟕
𝐜𝐦𝟐
¿Hence, the area of the remaining portion of the square is 57.714 cm2
𝟓𝟕 .𝟕𝟏𝟒𝐜𝐦𝟐
Problems based onAreas of combinations of plane figures
Chapter : Areas Related To Circles Website: www.letstute.com
Q) Four equal circles are described about the four corners of a square of side 14 cm so that each circle touches two others as shown in the figure. Find the area of the shaded region
Given: Side of a square = 14 cm
To find: Area of the shaded region = ?
Problems based onAreas of combinations of plane figures
A B
D C
14 cm
Chapter : Areas Related To Circles Website: www.letstute.com
Solution: Let ABCD represent the given square of side 14 cm.
Then, radius of each circle = r = = = 7 cm
Area of the shaded region = Area of square ABCD – Area of four quadrants
=
=A 7cm 7cm B
D 7cm 7cm C
7cm
7cm
7cm
7cm
Problems based onAreas of combinations of plane figures
= (196 – 154) cm2
= 𝟒𝟐𝐜𝐦𝟐
Chapter : Areas Related To Circles Website: www.letstute.com
Hence, the area of the shaded region is 42 cm2
A 7cm 7cm B
D 7cm 7cm C
7cm
7cm
7cm
7cm
Problems based onAreas of combinations of plane figures
Chapter : Areas Related To Circles Website: www.letstute.com
Q) Calculate the area of the shaded part in the figure. [Take
Given: AD = 7 cm DC = 24 cm
To find: Area of the shaded part = ?7 cm
24 cm
A B
D C
Problems based onAreas of combinations of plane figures
ADC =
Chapter : Areas Related To Circles Website: www.letstute.com
7 cm
24 cm
A B
D C
Solution: [Given]
𝐀𝐂𝐢𝐬 𝐭𝐡𝐞𝐝𝐢𝐚𝐦𝐞𝐭𝐞𝐫 𝐨𝐟 𝐭𝐡𝐞𝐜𝐢𝐫𝐜𝐥𝐞 .In the right angled triangle ADC, we have,
AC2 = AD2 + DC2 [Pythagoras’ Theorem]
AC2 = (7cm)2 + (24cm)2
AC2 = (49 + 576) cm2
AC2 = 625 cm2
AC = 25 cm
Problems based onAreas of combinations of plane figures
Chapter : Areas Related To Circles Website: www.letstute.com
Let r be the radius of the circle. Then, r = = = cm
= 12.5 cm
Area of the shaded part
=
= [3.14
= Area of the circle – Area of the rectangle
7 cm
24 cm
A B
D C
Problems based onAreas of combinations of plane figures
= (3.14)
Chapter : Areas Related To Circles Website: www.letstute.com
= (490.625 – 168)
= 𝟑𝟐𝟐 .𝟔𝟐𝟓𝐜𝐦𝟐
Hence, the area of the shaded part is 322.625 cm2
7 cm
24 cm
A B
D C
Problems based onAreas of combinations of plane figures
Chapter : Areas Related To Circles Website: www.letstute.com
Q) The given figure is a cross section which consists of a rectangle and two semi circles. From the information given, finda) Perimeter of the cross-sectionb) Area of the cross-section.
Given: Length of the rectangle = 28cm Breadth of the rectangle = 12cm
To find: a) Perimeter of the cross-sectionb) Area of the cross-section.
l=28cm
b=12cm
Problems based onAreas of combinations of plane figures
Chapter : Areas Related To Circles Website: www.letstute.com
Solution: Let the length and breadth of the rectangle be l and b respectively,
Let r be the radius of each semicircular part of the cross-section.
Then, l = 28 cm, b = 12 cm
And r = = cm = 14 cm
Problems based onAreas of combinations of plane figures
l=28cm
b=12cm
Chapter : Areas Related To Circles Website: www.letstute.com
a) Perimeter of the cross-section =
= 2
= 2(
= 2
= 2 (44 + 12) cm
=𝟏𝟏𝟐𝐜𝐦
Problems based onAreas of combinations of plane figures
l=28cm
b=12cm
Chapter : Areas Related To Circles Website: www.letstute.com
b) Area of the cross-section
= Area of the 2 semicircles + area of the rectangle= 2
=
= cm2
= 616 + 336
= 𝟗𝟓𝟐𝐜𝐦𝟐
Problems based onAreas of combinations of plane figures
l=28cm
b=12cm
Chapter : Areas Related To Circles Website: www.letstute.com
Hence, a) The perimeter of the cross-section is 112 cm
b) The area of the cross-section is
Problems based onAreas of combinations of plane figures
l=28cm
b=12cm
Chapter : Areas Related To Circles Website: www.letstute.com
Now we know…
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Problems based onAreas of combinations of plane figures
