{"id":75049,"date":"2022-03-21T13:01:01","date_gmt":"2022-03-21T13:01:01","guid":{"rendered":"https:\/\/reviews.tn\/wiki\/?p=75049"},"modified":"2022-03-21T13:01:01","modified_gmt":"2022-03-21T13:01:01","slug":"what-is-the-development-of-lateral-surface-of-a-cone","status":"publish","type":"post","link":"https:\/\/reviews.tn\/wiki\/what-is-the-development-of-lateral-surface-of-a-cone\/","title":{"rendered":"What is the development of lateral surface of a cone?","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p>The correct option is u201cCu201d. &#8220;When the curved surface of a cone is opened and laid on a plane, it shows the shape of a sector. &#8230; The radius of <b>the sector will be equal to the slant height<\/b> of the cone. The length of the arc will be equal to the circumference of the base of the cone, i.e. 2u03c0r.<\/p>\n<p>Similarly, How do you develop the surface of a cone? <iframe style=\"width: 640px; height: 460px;\" src=\"https:\/\/youtube.com\/embed\/_GMsF47TubU\" width=\"630\" height=\"455\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" data-original-w=\"720\" data-original-h=\"520\"><\/iframe><\/p>\n<p>What is the shape of the developed surface of a cone? One end of all the elements is at the vertex of the cone. The other ends describe a curved line. The base of the cone is <b>a circle<\/b>, with a circumference equal to the length of the curved line.<\/p>\n<p>Which method is used for development of lateral surface? <b>Parallel-line Method<\/b>: It is used for developing prisms and single curved surfaces like cylinders, in which all the edges\/generation of lateral surfaces are parallel in each other.<\/p>\n<p>Secondly What is meant by development of surfaces? \u201cThe development of surface of an object means <b>the unrolling and unfolding of all surfaces of the<\/b>. <b>object on a plane<\/b>.\u201d \u201cIf the surface of a solid is laid out on a plain surface, the shape thus obtained is called the.<\/p>\n<h2>What should be the angle of the development for a cone?<\/h2>\n<p>To calculate the dimensions of the development, first the slant height of the cone must be found from Pythagoras&#8217; theorem, ie R = \u221a [ H^2 + ( D\/2 )^2]. The sector angle \u03b8 is found from the formula <b>\u03b8 = D x ( 180 \/ R )<\/b>, which gives \u03b8 in degrees.<\/p>\n<p>then Which method is used for development of right cone? <b>Radial line method<\/b>:<\/p>\n<p> This method is used for pyramids and single curved surfaces like cones in which the apex is taken as a center and its slant edges or generator as the radius for its development.<\/p>\n<p>What are the different method of development of surfaces? <b>Parallel-line development<\/b>: Used for prisms, cylinders etc. in which parallel lines are drawn along the surface and transferred to the development. Radial-line development: Used for pyramids, cones etc. in which the true length of the slant edge or generator is used as radius.<\/p>\n<h2>How many types of surface development are there?<\/h2>\n<p>There are <b>three major<\/b> types of development followed by industries. Examples are shown in figure 2. Parallel line development: In this parallel lines are used to construct the expanded pattern of each three-dimensional shape.<\/p>\n<p>What is the slant height of cone? The slant height of an object (such as a cone, or pyramid) is <b>the distance along the curved surface, drawn from the edge at the top to a point on the circumference of the circle at the base<\/b>.<\/p>\n<p>How do you draw a surface development of a truncated cone?<\/p>\n<p><iframe style=\"width: 640px; height: 460px;\" src=\"https:\/\/youtube.com\/embed\/MOoAc_u6Sec\" width=\"630\" height=\"455\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" data-original-w=\"720\" data-original-h=\"520\"><\/iframe><\/p>\n<p>What are different methods of development of surfaces? <b>Parallel-line development<\/b>: Used for prisms, cylinders etc. in which parallel lines are drawn along the surface and transferred to the development. Radial-line development: Used for pyramids, cones etc. in which the true length of the slant edge or generator is used as radius.<\/p>\n<h2>What is the development of the lateral surface of a right cylinder on a sheet metal?<\/h2>\n<p><b>A=\u03c0r2<\/b>.<\/p>\n<p>What are the steps involved in development of lateral surface of cylinder?<\/p>\n<p>This can be done by the following steps: (i) <b>Draw right section as an edge in the front view per- pendicular to the fold lines<\/b>. (ii) Draw auxiliary plane perpendicular to the axis or fold line. (iii) The top view of the edge drawn in step (i), in the auxiliary plane will give the true size of the right section.<\/p>\n<p>Which method is used to develop pyramids and cones? Cones and pyramids are developed using <b>radial line development<\/b>. Radial line development is the process used for developing patterns for cones and pyramids. For the radial line method to be used, all lines must radiate from a common centre.<\/p>\n<p>What is the shape of the development of the lateral surface of the cylinder *? Explanation: In the case of a cylinder, the lateral surface when developed takes the shape of <b>a rectangle with length equal to the circumference of the base circle and breadth equal to the height of the cylinder<\/b>.<\/p>\n<h2>What is the shape of the development of lateral surface of the cylinder?<\/h2>\n<p>16. In gen- eral, the development of lateral surface of a cylinder is <b>a rec- langle having one side equal to the circumference of its base circle and the other equal to its length<\/b>. no told lines.<\/p>\n<p>What is the nature of the lateral surface of a cylinder? For a right circular cylinder of radius r and height h, the lateral area is the area of the side surface of the cylinder: <b>A = 2\u03c0rh<\/b>. For a pyramid, the lateral surface area is the sum of the areas of all of the triangular faces but excluding the area of the base.<\/p>\n<p>How do you find the lateral height of a cone?<\/p>\n<p>We can use the Pythagorean theorem, <b>a^2 + b^2 = c^2<\/b>, to calculate the slant height. For both cones and pyramids, a will be the length of the altitude and c will be the slant height. For a cone, b is the radius of the circle that forms the base.<\/p>\n<p>What is the difference between slant height and height of a cone? The vertical height (or altitude) which is the perpendicular distance from the top down to the base. The slant height which is the distance from the top, down the side, to a point on the <b>base circumference<\/b>.<\/p>\n<h3>What is the curved surface area of a cone?<\/h3>\n<p>The curved surface area of the cone can be given by finding the area of the sector by using the formula, Area of the sector (in terms of length of arc) = (arc length \u00d7 radius)\/ 2 = ((2\u03c0r) \u00d7 l)\/2 = \u03c0rl. \u2234 The curved surface area of a cone, <b>S = \u03c0rl units<sup>2<\/sup><\/b>. \u21d2 Total surface area of cone = \u03c0r<sup>2<\/sup> + \u03c0rl = \u03c0r (r + l).<\/p>\n<p>Which method of development is employed in case of cones? Which method of development is employed in case of cones? Explanation: Parallel-line method is employed in case of prisms and cylinders in which stretch out-line principle is used. <b>Radial-line development<\/b> is used for pyramids and cones in which the true length of the slant edge or the generator is used as a radius.<\/p>\n<p>What is truncated cone?<\/p>\n<p>Definition of truncated cone<\/p>\n<p> : <b>a cone section or pyramid lacking an apex and terminating in a plane usually parallel to the base<\/b>.<\/p>\n<p>How do you draw a cone layout? <iframe style=\"width: 640px; height: 460px;\" src=\"https:\/\/youtube.com\/embed\/OiM5DLR1kVc\" width=\"630\" height=\"455\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" data-original-w=\"720\" data-original-h=\"520\"><\/iframe><\/p>\n<h2>What is the lateral surface area of the cylinder?<\/h2>\n<p>For a right circular cylinder of radius r and height h, the lateral area is the area of the side surface of the cylinder: <b>A = 2\u03c0rh<\/b>. For a pyramid, the lateral surface area is the sum of the areas of all of the triangular faces but excluding the area of the base.<\/p>\n<p>What is lateral surface area of cuboid?<\/p>\n<p>The lateral surface area of a cuboid is <b>the combined surface area of the four vertical faces<\/b>. &#8230; The lateral surface area of cuboid will be, L= S = 2 (lb + bh + lh) &#8211; (2 \u00d7 l \u00d7 b) = (2 \u00d7 l \u00d7 h) + (2 \u00d7 b \u00d7 h) = 2h(l + b).<\/p>\n<p>What is the formula of lateral surface area of? Formulas for Lateral Surface Area<\/p>\n<p> length) <b>= 2 \u00d7 (lb + bh + hl)<\/b>. The total surface area of a cube is given by 6 \u00d7 (side)<sup>2<\/sup>. The lateral surface area of a cuboid is given by 2(length + breadth) \u00d7 height. Similarly, the lateral surface area of a cube of side \u201ca\u201d is equal to 4 \u00d7 (side)<sup>2<\/sup>.<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>The correct option is u201cCu201d. &#8220;When the curved surface of a cone is opened and laid on a plane, it shows the shape of a sector. &#8230; The radius of the sector will be equal to the slant height of the cone. The length of the arc will be equal to the circumference of the [&hellip;]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":9,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[8213],"tags":[],"class_list":["post-75049","post","type-post","status-publish","format-standard","hentry","category-science-math"],"jetpack_featured_media_url":"","jetpack-related-posts":[{"id":75050,"url":"https:\/\/reviews.tn\/wiki\/what-is-cone-development\/","url_meta":{"origin":75049,"position":0},"title":"What is cone development?","author":"Carole A. Cooper","date":"February 22, 2022","format":false,"excerpt":"The apex will remain in a fixed location, while the base will trace out a circular arc on the surface, with a length equal to the circumference of the cone's base. 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