2. SURFACE AREAS AND VOLUMES
INTRODUCTION
LENGTH
AREA
1 Centimeter (cm) = 10Milimeter
1 Decimeter (dm) = 10 Centimeter
1 Meter (m) = 10 dm = 100cm = 1000mm
1 kilometer (km) = 1000m = 100 dam = 10hm
1cm² = 10mm x 10mm = 100mm²
1m² = 1m x 1m = 10dm = 10dm =100dm²
1km²= 1km x 1km = 10hmx 10hm = 100hm²

3. Cuboid
A cuboid is a solid bounded by six rectangular plane regions.
Figure 1 is made of six rectangular plane region, namely ABCD,EFGH,AEHD,CGFB,DCGH and CDH
These six rectangular plane regions are six faces of the cuboid.
Any two faces other than the opposites faces are called adjacent faces
Edges
Any two adjacent faces of a cuboid meet in a line segment, which is called an edges of the cuboid .
1cm³= 1ml = 1cmx1cmx 1cm=
10mmx10mmx10mm=
1000mm³
1litre= 1000ml = 1000cm³

4. For any two edges that meet at and end-point, there is a third edge, that also meets them
that end-point. This point of intersection of three edges of a cuboid is called a vertex of the
cuboid.
BASE AND LATERAL FACES :
Any face of cuboid may be called the base of the cuboid. In that case the four faces which
meet the base are called the lateral faces of the cuboid.
CUBE
A cuboid whose length, breath and height are all equal is called a cube.
SURFACE AREA OF A CUBOID AND A CUBE.
Consider a cuboid whose length is l cm, breadth b cm and height h cm as shown in Fig-18.2
D C
A
h B
b H I G
E F

5.  Area of face ABCD = Area of face EFGH = (I x b) cm²
 Area of face AEHD = Area of face BFGC = (b x h) cm²
 Area of face ABFE = Area of face DHGC = (l x h) cm²
Total surface area of cuboid
= sum of the areas of all its six faces
= 2(lxb)+ 2(bxh) + 2(lxb)cm²
= 2(lxb+bxh+lxh)cm²
= 2(lb+bh+lh)cm²
Surface area of cube
Since all the 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 edge or side
or a cube, then
Surface area of the cube= 2(lxl+lxl+lxl)
=2x 3l² = 6(edge)²

6. LATERAL SURFACE AREA OF A CUBOID AND A CUBE
If out of the six faces of a cuboid, we only find the sum of the area of
four faces leaving the bottom and top faces. This sum is called the lateral
surface area of the cuboid.
(Consider a cuboid of length l, breadth b and height h as shown in Fig 18.3
D C
A B
h l
b G
E F
Fig..18.3
Lateral surface area of the cuboid
= Area of face AEHD + Area of face BFGC + Area of face ABFE + Area
of face DHGC
= 2 (b x h) + 2 (l x h)
= 2 (l +b) x h
= 2(Length + Breadth) x Height
= Perimeter of the base x Height
Lateral surface are of the cube = 2 (l xl +l x l) = 2 (l² + l²) = 4l² = 4 (Edge)²

7. SUMMARY Let there be a cuboid of length l, breadth b and
height h.
 (i) Total surface area of the cuboid = 2 (lb + bh + lh)
 (ii) Lateral surface area of the cuboid = 2 (l + b) h
 (iii) Diagonal of the cuboid = l² +b² +h²
 (iv) Length of all 12 edges of the cuboid = 4 (l + b + h)
If the length of each edge of a cube is 1 units, then
 (i) Total surface area of the cube = 6l²
 (ii) Lateral surface area of cube = 4l²
 (iii) Diagonal of the cube = 3l
 (iv) Length of all 12 edges of the cube = 12l

8. Now let discuss examples
Example – 1
Find the surface area of chalk box whose length, breadth and height are
16cm, 8 cm and 6cm,respectively.
SOLUTION
Clearly, chalk box is in the form of a cuboid
here l = 16cm, b = 8cm and h = 6cm
Surface area of the cuboid = 2 (lb + bh + lh)
= 2 (16 x 8 + 8x6 + 16 x 6)cm²
= 2 (128 + 48 + 96)cm² = 544cm²

9. Example – 2
Find the surface area of cube whose edge is 11cm
SOLUTION
We know that the surface area of the cube = 6 (Edge)²
Here edge = 11cm,
Surface area of given cube = 6 x (11)² cm² = (6x121)cm² = 726cm²
VOLUME OF A CUBOID
Measure of the space occupied by the cuboid
= Area of the rectangular sheet x h
= (l x b) x h = lbh
Hence, volume of the cuboid = lbh = Length x Breadth x Height

10. Right circular cylinder
A solid generated by the revolution of a rectangle about one of its sides is
called a right circular cylinder .
IMPORTANT POINTS
BASE : each of the circular ends on which the cylinder rests is called its
base.

11. AXIS : the line segment joining the centers of two circular bases is
called axis of the cylinder .
RADIES ;the radius of the cylinder base is called the radius of the cylinder
HEIGHT : the length of the axis of the cylinder is called the height of the
cylinder .
LATERAL SURFACE : the curved surface joining the two bases of ta right
circular cylinder is called its lateral surface.
FORMULA:
total surface area of the cylinder : 2rr(h+r)

12. RIGHT CIRCULAR CONE – A right circular cone is a solid generated by
revolving a line segment which passes through a fixed point and which
makes a constant angle with a fixed line.
The following are some terms related to a right circular cone.
VERTEX : The fixed point V is called the vertex of the cone.
AXIS : The fix line VO is called the axis of the cone.

13. HEIGHT : The length of the line segment joining the vertex to the centre
of the base is called the height of the cone.
SLANT HEIGHT : The length of the line segment joining the vertex to any
point on the circular edge of the base is called the slant height of the cone.
RADIUS : The radius OA of the base circle is called the radius of the
cone.
For a right circular cone of base radius r, slant height l and height h, we
have
(i) Curved surface area = r rl
(ii) Total surface area = r r (l+r)
(iii) Volume = 1/3 rr²h