PPt on surface areas of cube,cuboid, etc. suitable for class 9 or10

2. Group Members

3. arc length
sphere
parametric surfaces
calculus
partial derivatives double integration

4. Volume is the measure of the amount of space inside of a
solid figure, like a cube, ball, cylinder or pyramid. It's units
are always "cubic", that is, the number of little element
cubes that fit inside the figure.
The formula for the volume of a rectangular prism is:
Area = l x w x h
where:
l = length
w = width
h = height

5. Rectangular Pyramid
• Has rectangular base & 4
slanted faces.
• If the base is a square, &
if the apex lies directly
above a point at the
center of the base, then it
is a symmetrical
square pyramid.
S.A. = t2 + 2t √(s2 – t2/4)
V = Ah/3
s = slant height
t = edge of the base

6. The Cube
• It is a regular
hexahedron
• Has 12 edges & 6
faces
S.A. = 6s2
V = s3

7. CUBOID
• A hexahedron that
has 6 rectangular
faces.
• Has 12 edges but not
necessarily of the
same length.
Surface Area = 2lb + 2bh + 2hl
Volume = lbh
l
b
h

8. Cones and Cylinders
• A cone has a circular or
elliptical base and an
apex point.
• A cylinder has a circular
or elliptical base, & a
circular or elliptical top
that is congruent to the
base & that lies in a
plane parallel to the
base.
Right circular cone
Frustum of Right circular
cone
Slant circular cone
Right circular cylinder
Slant circular cylinder

9. The Right Circular Cone
• Has circular base
• Has an apex point
that lies on a line
perpendicular to the
plane of the base.
S.A. = Πrs, where s = √(r2 + h2)
= Πr √(r2 + h2)
S.A. = Πr2 + Πrs
= Πr2 + Πr√(r2 + h2)
V = Πr2 h/3
S
LATERAL AREA
SURFACE AREA OF THE CONE, INCLUDING THE BASE

10. Frustum of Right Circular Cone
• It is when a right
circular cone was
truncated by a plane
parallel to the base.
S.A. = Π(r2 + r2) √[h2 + (r2 – r1)2] + Π(r1
2 + r2
2),
where s = √[h2 + (r2 – r1)2], then
= Πs(r2 + r2) + Π (r1
2 + r2
2)
S.A. = Π(r1 + r2) √[h2 + (r2 – r1)2]
where s = √[h2 + (r2 – r1)2], then
= Πs(r1 + r2)
V = Πh( r1
2 +r1r2 + r2
2)/3
S.A. INCLUDING THE
TOP & THE BASE
S.A. EXCLUDING THE
TOP & THE BASE

11. The Slant Circular Cone
• Has circular base
• Has an apex point
that does not pass
through the center of
the base
V = Πr2 h/3
r
h

12. The Right Circular Cylinder
• Has circular base &
circular top.
• The base & the top lie
in a parallel planes
S.A. = 2Πrh + 2Πr2 or
= 2Πr (h + r)
S.A. = 2Πrh
V = Πr2 h
S.A. INCLUDING THE BASE
S.A. EXCLUDING THE BASE

13. The Slant Circular Cylinder
• It has circular base
and circular top
• The base & the top lie
in parallel planes
V = Πr2 h
r
h

14. The Sphere
These are geometric
solids with curve
spaces throughout.
Surface Area:
A = 4Πr2
Volume:
V = 4Πr3 /3
r