{"id":7324,"date":"2021-12-30T09:54:19","date_gmt":"2021-12-30T09:54:19","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=7324"},"modified":"2022-01-03T07:29:58","modified_gmt":"2022-01-03T07:29:58","slug":"concentric-circles-with-examples-and-faqs","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/concentric-circles-with-examples-and-faqs\/","title":{"rendered":"Concentric Circles with Examples and FAQs"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
\n” _builder_version=”4.11.3″ _module_preset=”default” header_font=”|700|||||||” header_text_align=”left” header_font_size=”50px” header_line_height=”1.18em” custom_padding=”|0px||4px|false|false” header_font_size_tablet=”” header_font_size_phone=”35px” header_font_size_last_edited=”on|phone” global_colors_info=”{}”]<\/p>\n

Concentric Circles with Examples and FAQs<\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

What are Concentric Circles?<\/b><\/h2>\n

The circles that share a common centre but have different radii are known as concentric circles.<\/span><\/p>\n

<\/span><\/p>\n

\"\"<\/span><\/p>\n

Concentric Circles<\/strong><\/em><\/p>\n

<\/span><\/p>\n

The figure represents concentric circles with a common centre\u2018 O\u2019.<\/span><\/p>\n

<\/span><\/p>\n

The region between the two concentric circles<\/b><\/h2>\n

\u00a0The region between the two concentric circles is called an annulus, which is a flat ring-like shape.<\/p>\n

The area of the annulus can be calculated easily by calculating the difference between the areas of the outer and inner circle.
<\/b><\/p>\n

\"\"<\/p>\n

Two concentric circles<\/i><\/b><\/p>\n

<\/span><\/p>\n

The above figure represents a pair of concentric circles, the radius of the outer circle is OC, and the radius of the inner circle is OA. Now the area of the ring: annulus, formed between the two circles can be calculated as follows:<\/span><\/p>\n

\\text { Let } O A=R \\text { and } O C=r<\/span><\/span><\/p>\n

Area of the circle with Radius \\mathrm{OA}=\\pi(O A)^{2}=\\pi R^{2}<\/span><\/span><\/p>\n


Area of the circle with Radius O C=\\pi(O C)^{2}=\\pi r^{2}<\/span><\/span><\/p>\n


\\therefore \\text{The area of the annulus }=\\pi R^{2}-\\pi r^{2}=\\pi\\left(R^{2}-r^{2}\\right) \\mid<\/span><\/span><\/p>\n

 <\/p>\n

Some Examples of Concentric Circle<\/b><\/h2>\n

<\/b><\/p>\n

\"\" \"\" \"\"<\/b><\/p>\n

<\/span><\/p>\n

A Ferris wheel, the wheel of a bicycle and a dartboard are some common examples of concentric circles.<\/span><\/p>\n

<\/span><\/p>\n

Example<\/b>:<\/span><\/p>\n

A playground is surrounded by a ring-like jogging track as shown in the figure. The inner radius of the ground is 8 m and the outer radius of the ground is 13 m. Find the area of the circular jogging track.<\/span><\/p>\n

\"\"<\/span><\/p>\n

<\/b><\/p>\n

Solution<\/b>:<\/span><\/p>\n

Given radius of the inner ground is 8 m and the outer radius of the ground is 12 m.<\/span><\/p>\n

Area of the inner ground\u00a0 =\\pi(8)^{2}=\\pi \\times 64=64 \\pi \\text{ }\\mathrm{m}^{2}<\/span><\/span><\/p>\n

The total area of the playground =\\pi(12)^{2}=\\pi \\times 144=144 \\pi \\text{ }\\mathrm{m}^{2}<\/span><\/span><\/p>\n

\u2234 the area of the jogging track\u00a0 =\\pi(144-64)=\\pi \\times 80=80 \\pi \\text{ } m^{2}<\/span><\/span><\/p>\n

The area of the jogging track is80 \\pi \\text{ } m^{2}<\/span>.<\/span><\/span><\/p>\n

[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics
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Explore Other Topics<\/h1>\n

[\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n

\n
Geometry<\/a><\/div>\n
Trigonometry<\/a><\/div>\n
Operations<\/a><\/div>\n
Numbers<\/a><\/div>\n<\/div>\n

[\/et_pb_text][et_pb_text admin_label=”Related Concepts
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Related Concepts<\/h1>\n

[\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n

\n
Area and Perimeter of Circle<\/a><\/div>\n
Area of Hollow Circle<\/a><\/div>\n
Area of Circular Ring<\/a><\/a><\/div>\n<\/div>\n

[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=”Row for space” _builder_version=”4.10.6″ _module_preset=”default” locked=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.11″ _module_preset=”default” global_colors_info=”{}”][et_pb_divider show_divider=”off” _builder_version=”4.10.4″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_divider][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ admin_label=”banner and faq Section” module_class=”mainsec2″ _builder_version=”4.10.4″ _module_preset=”default” custom_padding=”40px||0px||false|false” global_colors_info=”{}”][et_pb_row use_custom_gutter=”on” gutter_width=”1″ make_equal=”on” disabled_on=”on|on|off” admin_label=”banner Row” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fff7d6″ width=”100%” max_width=”1310px” height=”134px” custom_margin=”||50px||false|false” custom_padding=”12px||12px||true|false” border_radii=”on|11px|11px|11px|11px” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_image src=”https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/calloutImage.png” title_text=”calloutImage” show_bottom_space=”off” admin_label=”Image” module_class=”img1″ _builder_version=”4.10.8″ _module_preset=”default” width=”25px” height=”60px” custom_padding=”2px||2px||true|false” global_colors_info=”{}”][\/et_pb_image][et_pb_text module_class=”ftstyle” _builder_version=”4.9.10″ _module_preset=”default” text_orientation=”center” global_colors_info=”{}”]<\/p>\n

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Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n
    <\/ol>\n

    Q1. Do concentric circles intersect each other?
    <\/strong><\/h3>\n

    Ans: <\/strong>Concentric circles do not intersect each other. They share only the centre, other than that they have no points in common.
    <\/strong><\/span><\/span><\/p>\n

    Q2. How are concentric and congruent circles different?
    <\/strong><\/h3>\n

    Ans: <\/strong>Two or more circles that share a common centre but different radii are concentric, whereas two or more circles that have equal radii but different centres are congruent.<\/strong><\/p>\n

    Q3. How to calculate the Area of the Annulus?
    <\/strong><\/h3>\n

    Ans: <\/strong>The difference of the areas of two concentric circles gives the area of the annulus formed between them.<\/strong><\/strong><\/p>\n

    [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

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