Students can go through AP 9th Class Maths Notes Chapter 11 Surface Areas and Volumes to understand and remember the concepts easily.
Class 9 Maths Chapter 11 Notes Surface Areas and Volumes
→ Prism : A prism is a three dimensional solid which has identical faces at both ends. Its base and top are congruent polyhedrons.
We can name it by its base.
The faces of the prism are parallelograms or rectangles. Number of faces of prism is equal to its number of sides of base (or) top.
| No. of aides of its base | Name of Prism |
| 3 (triangle shape) | triangular prism |
| 4 sides equal | square prism |
| 4 (rectangular shape) | rectangular prism |
| 5 sides | pentagonal prism |
| 6 sides | hexagonal prism |
We can generate these prisms by staking up congruent figures.
→ Pyramid : A three dimensional shape whose base is a polygon, top (apex) is a point and sides (lateral faces) are triangulars is called Pyramid.
We name the Pyramid basing on the number of sides of the base Polygon. Ex : Triangular pyramid, rectangular pyramid, etc.
→ Cone : A three dimensional shape having a circular base and a point at top is called cone. Top point is called apex or vertex.
→ Right circular cone :
Right circular cone is a cone, whose axis falls perpendicular on the plane of base.
A cone can be formed by rotating any triangle by taking one of its two short sides (other than longest side) as the axis of rotation.
→ A Right circular cone can be formed by rotating a right triangle by taking one » of its legs as the axis of rotation.
→ Formulas related to cone :
1) Radius of base of cone = r
height of cone = h
Slant height of cone = l = \(\sqrt{\mathrm{r}^2+\mathrm{h}^2}\)
Then base area of cone – πr2
Circumference of base of cone = 2πr
Curved surface area of cone = πrl
Total surface area of cone
= C.S.A + base area
= πrl + πr2 = πr(l + r)
→ Sphere : Sphere is a 3-dimensional geometrical object, which is the set of all points which are at equal distances (r) from a given point (centre) in three dimensional space.
We can get a sphere by rotating a circle vertically along its diameter as rotation axis.
- A sphere is like surface of a ball.
- A sphere has only one curved surface.
- If a sphere is cut along its diameter each part we get is called hemisphere.
- A hemisphere will have 2 faces, that are one curved surface and one flat face i.e. circular face.
Formula for
i) Surface area of a sphere = 4πr2 (or) πd2
ii) Curved surface area of a hemisphere
= 2πr2 (or) \(\frac{\pi \mathrm{d}^2}{2}\)
iii) Total surface area of a hemisphere
= 3πr2 (or) \(\frac{3}{4}\) πd2
(where ‘r’ is radius of sphere and ‘d’ is diameter of sphere)
→ Volumes :
- Volume of a right circular cylinder = πr2h
- Volume of a right circular cone = \(\frac{1}{3}\) πr2h
- Volume of sphere (V) = \(\frac{4}{3}\) πr3
- Volume of a hemisphere
(V) = \(\frac{1}{3}\) × \(\frac{1}{3}\)πr3
= \(\frac{2}{3}\)πr3