Just some basic of the Chapter

1. AND VOLUMES

3.  DEFINATION:-A cuboid whose length ,breadth, height
are equal is called a cube.
 SOLID CUBE:-A solid cube is the part of the space
enclosed by six faces of the cube.

4.  A cube is a region of space formed by
six identical square faces joined along
their edges. Three edges join at each
corner to form a vertex.

5.  SURFACE AREA OF CUBE: Since all six faces of a cube
are squares of the same size i.e. For a cube we have l=b=h.
Thus, if l cm is the length of edge or side or a cube , then
 Therefore, surface area of a cube=6(a)square.

6.  A solid which has six rectangular
faces at right angles to each
other.

7.  Surface Area without theTop = 2 (bh + hl) + lb .
 Surface Area withoutTop & Base = 2 (bh + hl).
 Total Surface Area =2 (lb + bh + hl).

8. -T.S.A of a cube = 6a2.
-Lateral surface area of cube= 4(edge)sq.
-Volume of cube= (edge) cubic .
-T.S.A of a cuboid = 2(lb+bh+lh).
-L.S.A of a cuboid = 2 (l + b) h.
-Volume of the cuboid = lbh .

9.  A cylinder is one of the most basic curvilinear geometric shapes, the
surface formed by the points at a fixed distance from a given line
segment, the axis of the cylinder.
 The solid enclosed by this surface and by two planes perpendicular
to the axis is also called a cylinder.

10.  TSA of a cylinder = area of the base + area of
top + CSA of the cylinder
= ∏r2 + ∏r2 + 2∏rh
= 2∏r2 + 2∏rh
= 2∏r(r + h)
 Where, r is the radius
h is the height of the cylinder

11.  Volume of the cylinder = area of the base x
height
= r2 x h
=∏r2h
 Volume of hollow cylinder = ∏(R2 - r2) h
 Where, r is the radius and h is the height

12.  A cone is a three-dimensional geometric
shape that tapers smoothly from a flat base
(usually circular) to a point called the apex or
vertex.

13. TOTAL SURFACE AREA =curved surface area
+area of the base
= ∏rl+ ∏r2
+ = ∏r(r+l)
Curved surface area of cone =area of sector
=1/2 *l *(2 ∏r)
= ∏r l

14. 1.A sphere is a perfectly round geometrical object in three-dimensional space.
2. Hemisphere refers to the equal halves of the sphere and can also be called
the 3d design for a semi-circle.

15.  When we talk about
painting or polishing the
surface it is related to the
surface area.
 Surface-Area (TSA) = 4∏r2
 Where,
‘r’ is the radius
from the center to surface.

16.  When we talk about the air in the solid or
want to count the no. of small object from
the bigger one then it is related to the
volume.
 Volume of the sphere = 4/3∏r3
 Where, r is the radius.

17.  TSA of hemisphere = 3∏r2
 CSA of hemisphere = 2∏r2
 Where, ‘r’ is the radius.

18.  Volume of the Hemisphere = 2/3∏r3
 Where, r is the radius.