Maths Class 9 Notes for Volume and Surface （数学类9指出体积和表面）.pdfVIP

1 | P a g e Maths Class 9 Notes for Volume and Surface Area SOLIDS : The bodies occupying space (i.e. have 3-dimension) are called solids such as a cuboid, a cube, a cylinder, a cone, a sphere etc. VOLUME (CAPACITY) OFA SOLID: The measure of space occupied by a solid-body is called its volume. The units of volume are cubic centimeters (written as cm3) or cubic meters (written as m3). CUBOID: A solid bounded by six rectangular faces is called a cuboid. In the given figure, ABCDEFGH is a cuboid whose (i) 6 faces are : ABCD, EFGH, ABFE, CDHQ ADHE, and BCGF Out of these, the four faces namely ABFE, DCGH, ADHE and BCGF are called lateral faces of the cuboid. (ii) 12 edges are : AB, BC, CD, DA, EF, FG GH, HE, CG BF, AE and DH (iii) 8 vertices are : A, B, C, D, E, F, and H. Remark : A rectangular room is in the form of a cuboid and its 4 walls are its lateral surfaces. Cube : A cuboid whose length, breadth and height are all equal, is called a cube. A cube has 6 faces, each face is square, 12 edges, all edges are of equal lengths and 8 vertices. SURFACE AREA OF A CUBOID: Let us consider a cuboid of length = 1 units Breadth = b units and height = h units (Visit for all ncert solutions in text and videos, CBSE syllabus, note and many more) 2 | P a g e Then we have : (i) Total surface area of the cuboid =2(l * b + b * h + h * l) sq. units (ii) Lateral surface area of the cuboid = [2 (1 + b)* h] sq. units (iii) Area of four walls of a room = [2 (1 + b)* h] sq. units. = (Perimeter of the base * height) sq. units (iv) Surface area of four walls and ceiling of a room = lateral surface area of the room + surface area of ceiling =2(1+b)*h+l*b (v) Diagonal of the cuboid = √l2 + b2 + h2 SURFACE AREA OF A CUBE : Consider a cube of edge a unit. (i) The Total surface area of the cube = 6a2 sq. units (ii) Lateral surface area of the cube = 4a2 sq. units. (iii) The diagonal of the cube = √3 a units. SURFACE AREA OF THE RIGHT C