{"id":4754,"date":"2021-11-28T16:14:50","date_gmt":"2021-11-28T16:14:50","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=4754"},"modified":"2022-01-03T07:58:36","modified_gmt":"2022-01-03T07:58:36","slug":"perimeter-of-a-semicircle-mindspark","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/perimeter-of-a-semicircle-mindspark\/","title":{"rendered":"PERIMETER OF A SEMICIRCLE – MINDSPARK"},"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

PERIMETER OF A SEMICIRCLE – MINDSPARK<\/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

PERIMETER OF A SEMI-CIRCLE<\/b><\/b><\/h2>\n

Perimeter is nothing but the length of the boundary. A semicircle is the half of a circle so the perimeter of a semicircle is the length of the boundary as shown in the figure below:<\/span><\/p>\n

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

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

The black border is the boundary or the perimeter of the semicircle. O is the centre and the length from A to B through the centre is the diameter. The length from O to A is equal to the length from O to B and is the radius of the semicircle. Radius is equal to half the length of the diameter of the semicircle. <\/span><\/p>\n

 <\/p>\n

HOW TO FIND THE PERIMETER OF THE SEMICIRCLE?<\/b><\/h2>\n

It is easy to find the perimeter of the semicircle. We need to know the formula for the perimeter of a circle.\u00a0<\/span><\/p>\n

Perimeter of the circle = <\/span>2\u03c0r<\/span><\/p>\n

We will divide the perimeter by 2 to find the curved part of the semicircle which will give us<\/span><\/p>\n

\\frac{2 \\pi r}{2}=\\pi r<\/span><\/span><\/p>\n

When we find the perimeter of the semicircle, the boundary does not include the line AB which is the diameter. Here, in the case of the semicircle, we will need to include the diameter (denoted as d) as well since it counts as the boundary or the perimeter of the semicircle<\/span><\/p>\n

Perimeter of the semi-circle =\u00a0 <\/span>(<\/span>\u03c0r + d)<\/span><\/p>\n

Now, we know that d = 2r or diameter is twice the radius. Replacing the value of d<\/strong> we get,<\/span><\/p>\n

Perimeter of the semi-circle =\u00a0 <\/span>(<\/span>\u03c0r + 2r)<\/span><\/p>\n

Perimeter of the semi-circle =\u00a0 <\/span>r(\u03c0 <\/span>+ 2)<\/span><\/p>\n

Where the value of \u03c0 is<\/span> \\frac{22}{7} \\text { or } 3.14<\/span>\u00a0<\/span>which is a constant.<\/span><\/p>\n

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

EXAMPLES:<\/b><\/h2>\n

1. What will be the perimeter of a semicircle which has a radius of 7 cm?<\/b><\/p>\n

Ans:<\/strong> <\/span><\/b><\/p>\n

Perimeter of the semi-circle <\/span><\/b><\/p>\n

=7\\left[\\frac{22}{7}+2\\right]<\/span><\/span><\/b><\/p>\n

=7\\left[\\frac{22+14}{7}\\right]<\/span><\/span><\/b><\/p>\n

= 36 cm<\/span><\/p>\n

Therefore, the perimeter is 36 cm.<\/span><\/p>\n

2. Find the radius of the semicircle whose perimeter is 72 cm.<\/strong><\/p>\n

Ans:<\/strong> 72=r\\left[\\frac{22}{7}+2\\right]<\/span><\/span><\/p>\n

\\Rightarrow 72=r\\left[\\frac{22+14}{7}\\right]<\/span><\/span><\/p>\n

\\Rightarrow 72=r\\left[\\frac{36}{7}\\right]<\/span><\/span><\/p>\n

\\Rightarrow\\frac{(72)(7)}{36}=r<\/span><\/span><\/b><\/p>\n

\u2234 r = 14<\/span><\/p>\n

Therefore, the radius is 14 cm.<\/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
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\n

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

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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

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\n
Area of Semicircle<\/a><\/div>\n
Mensuration Formula<\/a><\/div>\n
Area and Perimeter of Circle<\/a><\/a><\/div>\n<\/div>\n

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

    Q1: What is the circumference of a semicircle?
    <\/strong><\/h3>\n

    Ans: <\/strong>Circumference or the perimeter of the semicircle is the length of its boundary.
    Perimeter of the semi-circle = r(\u03c0 + 2).<\/span><\/p>\n

    Q2. What is the formula for the circumference of a circle?<\/strong><\/h3>\n

    Ans: <\/strong>The formula for the perimeter or circumference of the circle is 2\u03c0r.<\/p>\n

    Q3. How to find the perimeter of the semicircle if the diameter is given?<\/strong><\/h3>\n

    Ans: <\/strong>Diameter is simply twice the radius. If we know the diameter, we can simply divide it by 2 <\/span>to find the radius and then put that in the formula of the perimeter of the semicircle.<\/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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