RBSE Class 9 Maths Notes Chapter 13 Surface Areas and Volumes

These comprehensive RBSE Class 9 Maths Notes Chapter 13 Surface Areas and Volumes will give a brief overview of all the concepts.

RBSE Class 9 Maths Chapter 13 Notes Surface Areas and Volumes

(A) Cuboid and Cube
Area
If in six parallel faces, all are rectangular, then it is called cuboid. Cuboid is also called rectangular face solid.

(1) Cuboid is also called right angular six parallel face. It has six faces.

(2) Two adjoining faces meet at same line segment which is called edges. A cuboid has 12 edges.

(3) A cuboid has eight vertices and opposite faces of cuboid are congruent (same) to each other.

(4) Formula of total surface area of a cuboid is – 2(l x b + b x h + hl) square unit.

(5) When length, breadth and height of cuboid are same then it is called cube. All the faces of cube are square and area of each face is same.

(6) Formula to find total surface area of cube  – = 6 (side)²

Diagonals of cube and cuboid –

(7) The line joimng the two opposite vertices of parallel face of cube or cuboids is called diagonal so there are 4 diagonals.

Volume
(1) Volume of cuboid is measured in cube unit.
(2) Formula for volume of cuboid — Length x breadth x height cube unit
(3) Volume of cube — Since length, breadth and height’ of cube are same, therefore formula for volume of cube is = (side)³ cube unit
(4) Units related to volume —
(i) 1 litre = 1000 cubic cm.
(ii) 1 cubic cm = 1000 cubic mm.
(iii) 1 cubic metre = 100,00,00 cubic cm.
(iv) 1 cubic metre = 1000 litre = 1 kilolitre

(B) Right circular cylinder: Surface Area and Volume
Right circular cylinder is a solid figure which have lateral curved surface and cross—sector and axis of cylinder is perpendicular to circular cross section:

General meaning –
(1) Here cylinder is used in the sense of right circular cylinder.
(2) When cylinder is kept in vertical form then circular ends is called base of cylinder and length of cylinder is called its height (h). Radius of circular end is called radius of cylinder.
(3) In hollow cylinder both the ends are open whereas in solid cylinder they are closed.

Area —
(1) Curved surface area of a solid cylinder = 2πrh
(2) Circumference of one end of a cylinder whose radius is r = 2πr
(3) Area of base of a cylinder = πr²
(4) Total surfaæ area of a cylinder = Curved surface Area + 2 x Area of base
= 2πrh+2πr²
= 2πr(h+r)

Volume —
(i) Volume of cylinder = πr²h

(C) Cone
Right circular cone is a solid figure which is obtained when a line segment revolve at a fixed point and from fixed line making constant angle.

General meaning —
(1) Shape of cone like a ice cream cone or joker cap.
(2) Height of right circular cone = h
Radius of cone = r and its slant
Height = l assumed.

Area —
(1) Formula of curved surface (slant surface) area of cone = 7trl
(2) Formula of total surface area of cone = πr (r + 1)

Volume —
(1) Volume of cone = \(\frac{1}{3} \pi r^{2} h\)
(2) Slant height of a cone l = \(l=\sqrt{r^{2}+h^{2}}\)

(D) Sphere
General Meaning –
(1) The solid generated on revolving a circle or semicircle about its diameter taking as axis is called sphere.
(2) Set of all the points in space are called sphere which are at equal distant from a fixed point.