{"id":155433,"date":"2022-05-02T10:30:44","date_gmt":"2022-05-02T05:00:44","guid":{"rendered":"https:\/\/www.aakash.ac.in\/blog\/?p=155433"},"modified":"2023-04-04T22:51:47","modified_gmt":"2023-04-04T17:21:47","slug":"cbse-10th-maths-revision-surface-areas-and-volumes-formulas","status":"publish","type":"post","link":"https:\/\/www.aakash.ac.in\/blog\/cbse-10th-maths-revision-surface-areas-and-volumes-formulas\/","title":{"rendered":"CBSE Class 10 Maths Term 2 Exam 2022: Revision Notes for Surface Areas and Volumes formulas"},"content":{"rendered":"

CBSE Class 10th board exams have commenced, and all that students need to do now is revision. Although preparing for the exams begins a year ago, what you revise before the exam has a huge impact on how you perform.\u00a0<\/span><\/p>\n

When the subject is Maths, revision before the exam becomes more important. Solving various problems of different types will boost your confidence. However, it is not possible to do that just before the exam. All you need to do before the exam is revise the important formulas that will help you solve the problems that will appear in the exam.\u00a0<\/span><\/p>\n

One chapter included in the CBSE class 10th<\/a> with many formulas to remember is ‘Surface Area and Volumes’. Remembering all the formulas from this chapter will ensure you secure all the marks in the exam. Read through the article to revise the chapter concerning your exam.<\/span><\/p>\n

Also See: CBSE Class 10 Maths Term 2 Important Chapters<\/a><\/p>\n

Overview of the chapter<\/h3>\n

CBSE class 10th Maths syllabus<\/a> has 15 chapters in all. A few chapters from the CBSE Class 10 syllabus<\/a> have many formulas to memorise. One such chapter is Surface area and Volumes. Memorising the formulas from this chapter can secure all the associated marks for this chapter. First of all, take a look at the concepts covered in this chapter.\u00a0<\/span><\/p>\n

The chapter deals with the surface areas and volumes of a few three-dimensional geometrical shapes. The chapter briefly describes the formulas of various three-dimensional shapes like cuboids, cubes, cylinders, cones, and spheres.\u00a0<\/span><\/p>\n

The chapter discusses the shapes’ total surface area, curved surface area, and lateral surface area, whichever is applicable. Read the article further for detailed notes for each shape individually. For a deep knowledge of the chapter, go through the <\/span>important concepts of Maths<\/span><\/a>.<\/span><\/p>\n

Surface area<\/h3>\n

2D faces form three-dimensional objects. Therefore, their surface areas are the sum of the areas of all the faces of the figure. Surface areas are generally categorised as:<\/span><\/p>\n

    \n
  1. Curved surface area: The area of the curved surfaces of the object form the curved surface area.<\/span><\/li>\n
  2. Lateral surface area: The area of all the faces of the object, excluding the top and bottom faces, is the lateral surface area.<\/span><\/li>\n
  3. Total surface area: The area of all the faces, including the bases, is called the total surface area.<\/span><\/li>\n<\/ol>\n

    Volume<\/h3>\n

    Volume is the space occupied by the three-dimensional object. Volume is usually the product of the three dimensions of the object and is therefore expressed in cubic units. Students should go through the <\/span>NCERT solutions for the CBSE class 10th Maths<\/span><\/a> to better understand the chapter. Go through the below given important formulas for surface areas and volumes.<\/span><\/p>\n

    Cuboid<\/h3>\n

    A cuboid is a three-dimensional object with a region covered with six rectangular faces.\u00a0<\/span><\/p>\n

    Surface Area of a Cuboid<\/h3>\n

    Consider a cuboid with dimensions as length l, breadth b and height h. The total surface area is the sum of the areas of all its six faces.<\/span><\/p>\n

    Therefore, the total surface area of a cuboid = 2(l\u00d7b) + 2(b\u00d7h) + 2(l\u00d7h)<\/span><\/p>\n

    = 2(lb + bh + lh)<\/span><\/p>\n

    The lateral surface area of the cuboid = 2(b\u00d7h) + 2(l\u00d7h)<\/span><\/p>\n

    = 2h(b\u00d7l)<\/span><\/p>\n

    Length of a diagonal of a cuboid =<\/span><\/p>\n

    \u221a(l<\/span>2<\/span> + b<\/span>2<\/span> + h<\/span>2<\/span>)<\/span><\/p>\n

    Volume of a Cuboid<\/h3>\n

    The volume of a cuboid<\/a> is the space occupied within its six faces.<\/span><\/p>\n

    Volume of a cuboid = (base area) \u00d7 height<\/span><\/p>\n

    = (lb) \u00d7 h = lbh<\/span><\/p>\n

    Cube<\/h3>\n

    A three-dimensional solid object with six square faces is a cube. It has twelve edges and eight vertices.<\/span><\/p>\n

    Surface area of a cube<\/h3>\n

    The length, breadth and height of a cube are all equal.\u00a0<\/span><\/p>\n

    Length = Breadth = Height = l<\/span><\/p>\n

    Therefore, the surface area of a cube =\u00a0<\/span><\/p>\n

    2 \u00d7 (3l<\/span>2<\/span>) = 6l<\/span>2<\/span><\/p>\n

    The lateral surface area = 2(l \u00d7 l + l \u00d7 l) = 4l<\/span>2<\/span><\/p>\n

    Diagonal of a cube =\u221a3l<\/span><\/p>\n

    Volume of a cube<\/h3>\n

    The volume of a cube = base area \u00d7 height = l<\/span>3<\/span><\/p>\n

    Cylinder<\/h3>\n

    A solid object with two circular faces connected with a lateral face forms a cylinder. It, therefore, has three faces.<\/span><\/p>\n

    Surface area of a cylinder<\/h3>\n

    Consider a cylinder of base radius r and height h. If opened along the diameter, the cylinder can be transformed into a rectangle of length 2\u03c0r and height h.\u00a0<\/span><\/p>\n

    Surface area of a cylinder of base radius r and height h =<\/span><\/p>\n

    2\u03c0 \u00d7 r \u00d7 h + (area of two circular bases)<\/span><\/p>\n

    = 2\u03c0rh + 2\u03c0r<\/span>2<\/span><\/p>\n

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

    Volume of a cylinder<\/h3>\n

    Volume of a cylinder = Base area \u00d7 height<\/span><\/p>\n

    = (\u03c0r<\/span>2<\/span>) \u00d7 h = \u03c0r<\/span>2<\/span>h<\/span><\/p>\n

    Cone<\/h3>\n

    A cone is a three-dimensional shape with one circular base that narrows down smoothly from the base to a single point, called a vertex.\u00a0<\/span><\/p>\n

    Surface area of a cone<\/h3>\n

    Consider a cone with a circular base of radius r, slant length l and height h.\u00a0<\/span><\/p>\n

    The curved surface area of this right circular cone is \u03c0rl.<\/span><\/p>\n

    The total surface area of the cone = Curved surface area + area of the base<\/span><\/p>\n

    = \u03c0rl + \u03c0r<\/span>2<\/span> = \u03c0r(l + r)<\/span><\/p>\n

    Volume of a cone<\/h3>\n

    Three cones of the same size form a cylinder of the same base and height.\u00a0<\/span><\/p>\n

    Therefore, the volume of a cone is \u2153 that of a cylinder of the same base and height.<\/span><\/p>\n

    The volume of a cone = =(1\/3)\u03c0r<\/span>2<\/span>h<\/span><\/p>\n

    Sphere<\/h3>\n

    A circular solid is a sphere, and all the points present are equidistant from the centre.<\/span><\/p>\n

    Surface area of a sphere<\/h3>\n

    For a sphere, the total surface area is the same as the curved surface area.\u00a0<\/span><\/p>\n

    The total surface area of a sphere = 4\u03c0r<\/span>2<\/span><\/p>\n

    Where r is the radius.<\/span><\/p>\n

    Volume of a sphere<\/h3>\n

    Volume of a sphere = (4\/3)\u03c0r<\/span>3<\/span><\/p>\n

    To properly practise various problems, go through the <\/span>previous years’ question papers<\/span><\/a> and <\/span>sample question papers<\/span><\/a>.<\/span><\/p>\n

    Conclusion<\/h3>\n

    Maths is a subject of immense importance considering the CBSE class 10th board exams. The score you get in the subject is critical when deciding a student’s career. It, therefore, becomes necessary to score well in Maths.\u00a0<\/span><\/p>\n

    Smart work and hard work are the keys to cracking any exam. When preparing for the CBSE class 10th board exams, it is important to consider which chapters can award you maximum marks and focus on them.\u00a0<\/span><\/p>\n

    The chapter Surface Area and Volume will give you marks easily as only a few formulas have a role to play in solving the questions from this chapter.\u00a0<\/span><\/p>\n

    It is advisable to memorise all the formulas from this chapter to hit the bullseye.\u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

    CBSE Class 10th board exams have commenced, and all that students need to do now is revision. Although preparing for the exams begins a year ago, what you revise before the exam has a huge impact on how you perform.\u00a0 When the subject is Maths, revision before the exam becomes more important. Solving various problems […]<\/p>\n","protected":false},"author":1,"featured_media":138667,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3581],"tags":[1568,2814],"class_list":["post-155433","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse","tag-cbse-class-10","tag-class-10-maths"],"yoast_head":"\nCBSE Class 10 Maths Term 2 Exam 2022: Revision Notes for Surface Areas and Volumes formulas<\/title>\n<meta name=\"description\" content=\"CBSE Class 10 Maths Term 2 Exam 2022: Check out mathematics chapter Surface Areas and Volumes formulas revision notes, important questions with answers for term 2 exam and more on aakash.ac.in\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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