{"id":3260,"date":"2021-10-13T08:53:09","date_gmt":"2021-10-13T08:53:09","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=3260"},"modified":"2022-01-02T07:04:00","modified_gmt":"2022-01-02T07:04:00","slug":"right-circular-cylinder","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/right-circular-cylinder\/","title":{"rendered":"RIGHT CIRCULAR CYLINDER"},"content":{"rendered":"

[et_pb_section fb_built=”1″ 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” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.6″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|0px|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
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RIGHT CIRCULAR CYLINDER- MEANING, FORMULAE AND ILLUSTRATION<\/strong><\/h1>\n

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Every one of you has purchased a beverage can from the shop. Have you ever thought of the shape of that can? The shape of the can is like a right circular cylinder. There are many examples in our surroundings that have a cylindrical shape. So, In this article, we are going to learn about the meaning and formation of the right circular cylinder, its properties, its surface area & volume, some real-life examples and illustrations.<\/p>\n

RIGHT CIRCULAR CYLINDER<\/strong><\/h2>\n

 <\/p>\n

MEANING OF RIGHT CIRCULAR CYLINDER<\/strong><\/h3>\n

A right circular cylinder is formed by rotating a rectangle about one of its sides as an axis. It is a three-dimensional solid that consists of 2 parallel circular bases that are connected by a closed circular surface in which every base is in the form of a circular disk and each of the circular bases has a similar radius and are parallel to each other. The line passing through the middle of the right circular cylinder is called the axis and the axis of the cylinder conjoins the middle of the 2 circular bases of the cylinder. The perpendicular distance between both the circular bases is called the height of the right circular cylinder, which is represented by \u201ch\u201d in the given figure. The distance from the centre of the circular bases towards its outer boundary is called the radius, which is represented by \u201cr\u201d in the given figure.<\/p>\n

 <\/p>\n

\"\"<\/p>\n

 <\/p>\n

PROPERTIES OF RIGHT CIRCULAR CYLINDER<\/strong><\/h2>\n

1) The line that joins the circular base from the centre is the axis.<\/p>\n

2) If a plane cuts the right circular cylinder horizontally parallel to the bases, then the intersection is a circle.<\/p>\n

3) To specify a right circular cylinder, we need to know only its radius and its height.<\/p>\n

4) The axis forms 90 degrees with circular bases.<\/p>\n

 <\/p>\n

SURFACE AREA OF RIGHT CIRCULAR CYLINDER<\/strong><\/h2>\n

The surface space of a right circular cylinder is the total area lined by the surface of it. There are 2 types of surface areas of a right circular cylinder-:<\/p>\n

 <\/p>\n

1. Lateral or Curved surface area<\/strong><\/h3>\n

It is the area of the cylinder excluding the areas of its circular bases. When the cylinder is opened from both ends then the curved surface area is calculated.<\/p>\n

Formula<\/strong><\/p>\n

Curved surface area (CSA) = Circumference of circular base \u00d7 height<\/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 \u00a0= 2\u03c0r \u00d7 h<\/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 \u00a0= 2\u03c0rh sq. units.<\/p>\n

 <\/p>\n

2. Total surface area<\/strong><\/h3>\n

It is the area covered by its curved surface and the two circular bases. When the cylinder is closed from both ends then the total surface area is calculated.<\/p>\n

Formula<\/strong><\/p>\n

Total surface area (TSA) = Curved surface area + 2(Area of a circle)<\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 2\u03c0rh + 2\u03c0r2<\/sup><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 2\u03c0r(h+r) sq. units.<\/p>\n

 <\/p>\n

VOLUME AND FORMULA<\/strong><\/h2>\n

It is the measure of the space occupied by the whole cylinder. The quantity is measured in cubic units.<\/p>\n

Formula<\/strong><\/p>\n

Volume = Area of the circular disks x Height of the right circular Cylinder<\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= \u03c0r2<\/sup> \u00d7 h<\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= \u03c0r2<\/sup>h cubic units<\/p>\n

 <\/p>\n

FORMATION OF A RIGHT CIRCULAR CYLINDER<\/strong><\/h2>\n

When a rectangle is revolved about one of its sides, it forms the right circular cylinder. So, for the formation of a right circular cylinder, we need a rectangular sheet.<\/p>\n

We will follow various steps for learning the formation of a right circular cylinder-<\/p>\n

STEP 1<\/strong> – We will take a rectangular sheet as given in the figure.<\/p>\n

 <\/p>\n

\"\"<\/p>\n

 <\/p>\n

STEP 2<\/strong> – Now, we will fold the rectangular sheet along with one of its sides(length) until the other two sides(breadth) merge.<\/p>\n

 <\/p>\n

\"\"<\/p>\n

 <\/p>\n

STEP 3<\/strong> – You will observe that after folding, the shape that is formed is a right circular cylinder. The length of the rectangle is equal to the circumference of the circular base and the breadth of the rectangle is equal to the height of the cylinder. The curved or lateral surface area of the cylinder is equal to the area of a rectangle,<\/p>\n

Where length = 2\u03c0r = Circumference of the circular base(where r is the radius of the base.)<\/p>\n

and breadth = h.<\/p>\n

The curved surface area of cylinder = 2\u03c0rh = length(l)\u00d7breadth(b) = area of rectangular sheet used<\/p>\n

 <\/p>\n

\"\"<\/p>\n

 <\/p>\n

<\/h2>\n

ILLUSTRATIONS<\/strong><\/h2>\n

Q1.\u00a0 The radius of the base of the solid right circular cylinder is 10 cm and has a height of 20 cm. What’s its total surface area?<\/strong><\/p>\n

Sol.-<\/strong><\/p>\n

Total surface area = 2\u03c0rh + 2\u03c0r2<\/sup><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0=2\u03c0r(h + r)<\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0=2\u00d7 3.14\u00d710(20 + 10)<\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 1885.71 cm2<\/sup>.<\/p>\n

 <\/p>\n

Q2. What is going to be the quantity of a right circular cylinder, if the radius of the base is 20 centimetres and the height of the cylinder is 30 centimetres. (Given \u03c0= 3.14)<\/strong><\/p>\n

Sol.-<\/strong>\u00a0<\/p>\n

Volume of a right cylinder = \u03c0r2<\/sup> h<\/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 \u00a0= 3.14 \u00d7 202<\/sup> \u00d7 30<\/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 \u00a0= 3.14 \u00d7 400 \u00d7 30<\/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 \u00a0<\/strong>= 37680 cm3<\/sup><\/p>\n

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Explore Other Topics<\/h1>\n

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\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

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Surface Area and Volume Formulas<\/a><\/div>\n
CSA of Cylinder<\/a><\/a><\/div>\n

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Frequently Asked Questions<\/h1>\n

Q1<\/strong>. Why is it called a right circular cylinder?<\/strong><\/p>\n

Ans<\/strong>. When the axis of the cylinder makes a right angle to its circular base, then the cylinder is called a right circular cylinder.<\/p>\n

Q2<\/strong>. What are some real-life examples of cylinders?<\/strong><\/p>\n

Ans<\/strong>. Toilet paper rolls, beverage cans, torches etc. are some real-life examples of a cylinder.<\/p>\n

Q3<\/strong>. What is the perimeter of the right circular cylinder?<\/strong><\/p>\n

Ans<\/strong>. The lateral or curved surface area of the cylinder is the perimeter of the cylinder. The formula for curved surface area is 2\u03c0rh, where r is the radius of the circular base and h is the height of the cylinder<\/p>\n

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RIGHT CIRCULAR CYLINDER- MEANING, FORMULAE AND ILLUSTRATIONEvery one of you has purchased a beverage can from the shop. Have you ever thought of the shape of that can? The shape of the can is like a right circular cylinder. There are many examples in our surroundings that have a cylindrical shape. So, In this article, […]<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":714,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"yoast_head":"\nRIGHT CIRCULAR CYLINDER - mydomain<\/title>\n<meta name=\"description\" content=\"A right circular cylinder is formed by rotating a rectangle about one of its sides. 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