{"id":8569,"date":"2020-12-04T09:29:51","date_gmt":"2020-12-04T03:59:51","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=8569"},"modified":"2020-12-04T09:48:10","modified_gmt":"2020-12-04T04:18:10","slug":"cones","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/cones\/","title":{"rendered":"Cones"},"content":{"rendered":"

Cones<\/span><\/h2>\n

Cones<\/strong> are three-dimensional closed surfaces.<\/p>\n

In general use, the term cone refers to a right circular cone with its end closed to form a circular base surface. The vertex of the cone (the point) is not in the same plane as the base.
\n\"ConesCones are not<\/strong> called polyhedra since their faces are not polygons. In many ways, however, a cone is similar to a pyramid. A cone’s base is simply a circle rather than a polygon as seen in the pyramid.<\/p>\n

The volume<\/strong> of a cone can be calculated in the same manner as the volume of a pyramid: the volume is one-third the product of the base area times the height of the cone,
\n\\(V=\\frac { 1 }{ 3 } Bh\\)
\nSince the base of a cone is a circle, the formula for the area of a circle can be substituted into the volume formula for B :
\n\\(V=\\frac { 1 }{ 3 } \\pi { r }^{ 2 }h\\)
\n(Volume of a cone: r = radius, h = height)<\/p>\n

A net is a two-dimensional figure that can be cut out and folded up to make a three-dimensional solid.
\n\"ConesLateral = any face or surface that is not a base.<\/p>\n

In a right circular cone, the slant height, s, can be found using the Pythagorean Theorem:\u00a0\\(s=\\sqrt { { r }^{ 2 }+{ h }^{ 2 } } \\)<\/p>\n

The surface area<\/strong> (of a closed cone) is a combination of the lateral area and the area of the base. When cut along the slant side and laid flat, the surface of a cone becomes one circular base and the sector of a circle (lateral surface), as shown in the net at the left.<\/p>\n

Note that the length of the arc in the sector is the same as the circumference of the small circular base.
\nBy using a proportion, the area of the sector (lateral area) will be:
\n\"ConesThe lateral area (sector) = s\u03c0r<\/strong>
\nThe base area = area of a circle
\nSA = s\u03c0r + \u03c0r2<\/sup><\/strong> (Total Surface Area of a Closed Cone)<\/p>\n

Note:<\/strong> The formula for the area of the sector (lateral area), , is equal to one half the product of the slant height and the circumference of the base.
\n\"Cones<\/p>\n

When working with surface areas of cones, read the questions carefully.
\n\"Cones<\/p>\n","protected":false},"excerpt":{"rendered":"

Cones Cones are three-dimensional closed surfaces. In general use, the term cone refers to a right circular cone with its end closed to form a circular base surface. The vertex of the cone (the point) is not in the same plane as the base. Cones are not called polyhedra since their faces are not polygons. […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[3129,3130,3128],"yoast_head":"\nCones - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/cones\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Cones\" \/>\n<meta property=\"og:description\" content=\"Cones Cones are three-dimensional closed surfaces. In general use, the term cone refers to a right circular cone with its end closed to form a circular base surface. The vertex of the cone (the point) is not in the same plane as the base. Cones are not called polyhedra since their faces are not polygons. 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