{"id":6940,"date":"2021-12-28T08:59:47","date_gmt":"2021-12-28T08:59:47","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=6940"},"modified":"2022-01-03T06:54:19","modified_gmt":"2022-01-03T06:54:19","slug":"area-of-a-hollow-circle-solved-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/area-of-a-hollow-circle-solved-examples\/","title":{"rendered":"Area of a hollow circle \u2013 Solved Examples"},"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

Area of a hollow circle \u2013 Solved Examples<\/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

Area of a hollow circle<\/b><\/h2>\n

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

A hollow circle is also known as a circular ring or annulus. It consists of two concentric circles. The radius of these circles are different from each other<\/p>\n

In the figure given below, it can be seen that the measure of the region between the two concentric circles is equal to the area of a hollow circle. The radius of the bigger circle and the smaller circle are R_{1} \\text { and } R_{2}<\/span>respectively.
<\/b><\/p>\n

 <\/p>\n

\"\"<\/p>\n

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

In order to find the area of the circular ring, we have to subtract the area of the smaller circle from the area of the bigger circle.<\/span><\/p>\n

\\text { Area }=\\pi\\left(R_{1}{ }^{2}-R_{2}{ }^{2}\\right)<\/span><\/span><\/p>\n

The area of the hollow circle is actually the area of the base of a hollow cylinder.<\/span><\/p>\n

Derivation of the formula<\/strong><\/p>\n

We know that,\u00a0<\/span><\/p>\n

Area of the bigger circle having radius \\mathrm{R}_{1}=\\pi \\times \\text { radius }^{2}=\\pi R_{1}^{2}<\/span><\/span><\/p>\n

Area of the smaller circle having radius \\mathrm{R}_{2}=\\pi \\times \\text { radius }^{2}=\\pi R_{2}^{2}<\/span><\/span><\/p>\n

Area of the hollow circle = Area of the bigger circle \u2013 Area of the smaller circle<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= \\pi R_{1}^{2}-\\pi R_{2}^{2} <\/span><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= \\pi\\left(R_{1}^{2}-R_{2}^{2}\\right) <\/span><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= \\pi\\left(R_{1}+R_{2}\\right)\\left(R_{1}-R_{2}\\right)<\/span><\/span><\/p>\n

\u00a0Hence it is proved that the area is equal to \\pi\\left(R_{1}^{2}-R_{2}^{2}\\right)<\/span><\/span><\/p>\n

 <\/p>\n

Solved Examples<\/b><\/h2>\n

1. Find the area of a hollow circle having an inner radius of 11 cm and an outer radius of 19 cm?<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

Outer Radius=R_{1}=19 \\mathrm{~cm}<\/span><\/span><\/p>\n

Inner Radius =\\mathrm{R}_{2}=11 \\mathrm{~cm}<\/span><\/span><\/p>\n

Area =\\pi\\left(R_{1}{ }^{2}-R_{2}{ }^{2}\\right)<\/span><\/span><\/p>\n

=\\pi\\left(19^{2}-11^{2}\\right)=\\pi(361-121) =753.98 \\mathrm{~cm}^{2}<\/span><\/span><\/p>\n

Hence the area is equal to 753.98 \\mathrm{~cm}^{2}<\/span>.<\/span><\/p>\n

 <\/p>\n

2. The area of the base of a hollow cylinder is equal to 506 m\u00b2. If the outer radius of the cylinder is equal to 15 m. Find the inner radius.<\/strong><\/p>\n

Solution:<\/strong><\/p>\n

The base of a cylinder is a hollow circle<\/span><\/p>\n

\\text{ Outer radius} =R_{1}=15 \\mathrm{~m}<\/span><\/span><\/p>\n\\text { Area } =506 m^{2} <\/span>\n


\\text { Area } =\\pi\\left(R_{1}{ }^{2}-R_{2}{ }^{2}\\right) <\/span><\/span><\/p>\n


\\Rightarrow 506=\\pi\\left(15^{2}-R_{2}{ }^{2}\\right) <\/span><\/span><\/p>\n


\\Rightarrow \\mathrm{R}_{2}=8 \\mathrm{~m}<\/span>
<\/span><\/p>\n

The inner radius is equal to 8 m.<\/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

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

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\n
Mensuration Formula<\/a><\/div>\n
Surface Area and Volume Formula<\/a><\/div>\n
Concentric Circles<\/a><\/a><\/div>\n<\/div>\n

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

    Q1. What do you mean by a hollow circle?
    <\/strong><\/h3>\n

    Ans: <\/strong>A hollow circle is also known as a circular ring or annulus. It consists of two concentric circles. The radius of one circle is greater than the radius of the other circle.
    <\/strong><\/span><\/span><\/p>\n

    Q2. Is there any difference between a ring and a hollow circle?
    <\/strong><\/h3>\n

    Ans: <\/strong>No, A hollow circle is also known as a circular ring.
    <\/strong><\/strong><\/p>\n

    Q3. What is the area of a hollow circle?<\/strong><\/h3>\n

    Ans: <\/strong>The area of a hollow circle is given by the formula \\pi\\left(R_{1}^{2}-R_{2}^{2}\\right) \\text {, where } R_{1} \\text { and } R_{2}<\/span><\/span>are the radius of the bigger circle and smaller circle respectively.<\/span><\/p>\n

    <\/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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