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.
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.
One chapter included in the CBSE class 10th 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.
Overview of the chapter
CBSE class 10th Maths syllabus has 15 chapters in all. A few chapters from the CBSE Class 10 syllabus 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.
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.
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 important concepts of Maths.
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:
- Curved surface area: The area of the curved surfaces of the object form the curved surface area.
- Lateral surface area: The area of all the faces of the object, excluding the top and bottom faces, is the lateral surface area.
- Total surface area: The area of all the faces, including the bases, is called the total surface area.
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 NCERT solutions for the CBSE class 10th Maths to better understand the chapter. Go through the below given important formulas for surface areas and volumes.
A cuboid is a three-dimensional object with a region covered with six rectangular faces.
Surface Area of a Cuboid
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.
Therefore, the total surface area of a cuboid = 2(l×b) + 2(b×h) + 2(l×h)
= 2(lb + bh + lh)
The lateral surface area of the cuboid = 2(b×h) + 2(l×h)
Length of a diagonal of a cuboid =
√(l2 + b2 + h2)
Volume of a Cuboid
The volume of a cuboid is the space occupied within its six faces.
Volume of a cuboid = (base area) × height
= (lb) × h = lbh
A three-dimensional solid object with six square faces is a cube. It has twelve edges and eight vertices.
Surface area of a cube
The length, breadth and height of a cube are all equal.
Length = Breadth = Height = l
Therefore, the surface area of a cube =
2 × (3l2) = 6l2
The lateral surface area = 2(l × l + l × l) = 4l2
Diagonal of a cube =√3l
Volume of a cube
The volume of a cube = base area × height = l3
A solid object with two circular faces connected with a lateral face forms a cylinder. It, therefore, has three faces.
Surface area of a cylinder
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 2πr and height h.
Surface area of a cylinder of base radius r and height h =
2π × r × h + (area of two circular bases)
= 2πrh + 2πr2
Volume of a cylinder
Volume of a cylinder = Base area × height
= (πr2) × h = πr2h
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.
Surface area of a cone
Consider a cone with a circular base of radius r, slant length l and height h.
The curved surface area of this right circular cone is πrl.
The total surface area of the cone = Curved surface area + area of the base
= πrl + πr2 = πr(l + r)
Volume of a cone
Three cones of the same size form a cylinder of the same base and height.
Therefore, the volume of a cone is ⅓ that of a cylinder of the same base and height.
The volume of a cone = =(1/3)πr2h
A circular solid is a sphere, and all the points present are equidistant from the centre.
Surface area of a sphere
For a sphere, the total surface area is the same as the curved surface area.
The total surface area of a sphere = 4πr2
Where r is the radius.
Volume of a sphere
Volume of a sphere = (4/3)πr3
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.
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.
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.
It is advisable to memorise all the formulas from this chapter to hit the bullseye.