A cross-section of a cylinder is nothing but when you cut the slice in a cylinder you can see a circular base in it. That sliced part is known as the cross-section. The top view of the cross-section cylinder looks like a circle. Follow this article to know more about the cross-section and its formulas with examples.<\/p>\n
A cross-section is a plane section. It means putting an object into pieces creates many parallel cross-sections.
\nArea of cross section = Ac = \u03c0 \u00d7 (D\u00b2 – d\u00b2)\/4<\/p>\n
The cross-sectional area of the cylinder is equal to the area of the circle if it is cut parallel to the circular base. It is obtained by the three-dimensional cylinder<\/a>. There are two ways to calculate the cross-sectional area of a cylinder they are lateral surface area and total surface area.<\/p>\n The volume of the cylinder means calculating the total amount of space occupied by the cross-sectioned part of the cylinder. The volume of the cross-section of the cylinder is the product of the surface area and height of the cylinder.<\/p>\n See More:<\/p>\n Example 1.<\/strong> Example 2.<\/strong> Example 3.<\/strong> Example 4.<\/strong> Example 5.<\/strong> 1. What are the units for cross-sectional area?<\/strong><\/p>\n The units for cross-sectional area is square units.<\/p>\n 2. Does a cylinder have a cross section?<\/strong><\/p>\n The formula at the top of the page can be used to find the volume of a cylinder because a cylinder has a constant cross-sectional area if it is sliced parallel to the circular face.<\/p>\n 3. How do you find cross sections?<\/strong><\/p>\n The volume of any rectangular solid, including a cube, is the area of its base multiplied by its height: V = l \u00d7 w \u00d7 h. Therefore, if a cross section is parallel to the top or bottom of the solid, the area of the cross-section is l \u00d7 w.<\/p>\n","protected":false},"excerpt":{"rendered":" A cross-section of a cylinder is nothing but when you cut the slice in a cylinder you can see a circular base in it. That sliced part is known as the cross-section. The top view of the cross-section cylinder looks like a circle. Follow this article to know more about the cross-section and its formulas … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143808"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=143808"}],"version-history":[{"count":2,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143808\/revisions"}],"predecessor-version":[{"id":143811,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143808\/revisions\/143811"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=143808"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=143808"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=143808"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Volume of a Cross Section<\/h3>\n
Formulas on Cross Section<\/h3>\n
\n
\n= A \u00d7 h<\/li>\n
\n= P \u00d7 h<\/li>\n
\n= P \u00d7 h + 2 \u00d7 A
\nwhere P = perimeter of the cross-section
\nh = height
\nA = Area of the cross-section<\/li>\n<\/ul>\n\n
Cross Section Examples<\/h3>\n
\nA Hollow pipe of inner radius 3 cm and outer radius 4 cm is melted and changed into a solid right circular cylinder of the same length as that of the pipe. Find the area of the cross-section of the solid cylinder.
\nSolution:<\/strong>
\nGiven that
\nInner radius of the hollow pipe = r = 5 cm
\nOuter radius of the hollow pipe = R = 6 cm
\nWe know that,
\nThe area of the cross of the pipe = \u03c0( R\u00b2 – r\u00b2)
\n= \u03c0(6\u00b2 – 5\u00b2) cm\u00b2
\n= \u03c0(36 – 25) cm\u00b2
\n= 9\u03c0 cm2
\nTherefore, the volume of the pipe = (Area of the cross section) \u00d7 length
\n= 9\u03c0 \u00d7 h cm\u00b3
\n(Taking length of the pipe = h cm)
\n= 9\u03c0h cm\u00b3
\nThe volume of the right circular cylinder = \u03c0r\u00b2h cm\u00b3
\n(Taking the radius of the cross section of the cylinder = r cm)
\nThe two volumes are equal so
\nTherefore, 9\u03c0h cm\u00b3 = \u03c0r\u00b2h cm\u00b3
\nr\u00b2 = 9
\nTherefore, the area of the cross section of the solid cylinder
\n=\u03c0r\u00b2 cm\u00b2
\n= 22\/7 \u00d7 9 cm\u00b2
\n= 28.26 cm\u00b2<\/p>\n
\nFind the cross-sectional area of a plane perpendicular to the base of a cube of volume equal to 27 cm\u00b3.
\nSolution:<\/strong>
\nGiven that
\nVolume of cube = Side\u00b3
\nTherefore,
\nSide\u00b3 = 27
\nSide = 3 cm
\nThe cross-section of the cube will be a square. Therefore, the side of the square is 3cm.
\nHence, cross-sectional area = a\u00b2 = 3\u00b2 = 9 sq.cm.<\/p>\n
\nDetermine the cross-section area of the given cylinder whose height is 20 cm and radius is 6 cm.
\nSolution:<\/strong>
\nGiven that
\nRadius of a cylinder = 6 cm
\nHeight of a cylinder = 20 cm
\nWe know that
\nWhen the plane cuts the cylinder parallel to the base, then the cross-section obtained is a circle.
\nTherefore, The area of a circle, A = \u03c0r\u00b2 square units.
\nWhere
\n\u03c0 = 3.14
\nA = 3.14 (6)\u00b2 cm\u00b2
\nA = 3.14 (36) cm\u00b2
\nA = 113.04 cm\u00b2
\nThus, the cross section area of the cylinder is 113.04 cm\u00b2<\/p>\n
\nFind the cross-sectional area of a plane perpendicular to the base of a cube of volume equal to 8 cm\u00b3.
\nSolution:<\/strong>
\nGiven that
\nVolume of cube = Side\u00b3
\nTherefore,
\nSide\u00b3 = 8
\nSide = 2 cm
\nThe cross-section of the cube will be a square. Therefore, the side of the square is 2 cm.<\/p>\n
\nDetermine the cross-section area of the given cylinder whose height is 40 cm and radius is 3 cm.
\nSolution:<\/strong>
\nGiven that
\nRadius of a cylinder = 3 cm
\nHeight of a cylinder = 40 cm
\nWe know that
\nWhen the plane cuts the cylinder parallel to the base, then the cross-section obtained is a circle.
\nTherefore, The area of a circle, A = \u03c0r\u00b2 square units.
\nWhere
\n\u03c0 = 3.14
\nA = 3.14 (3)\u00b2 cm\u00b2
\nA = 3.14 (9) cm\u00b2
\nA = 28.26 cm\u00b2
\nThus, the cross section area of the cylinder is 28.26 cm\u00b2<\/p>\nFAQs on Cross Section of Cylinder<\/h3>\n