This document defines and provides information about common 3D shapes including cubes, cuboids, cylinders, cones, spheres, hemispheres, and frustums. It describes their key properties such as the number of faces, edges, and vertices. It also provides formulas to calculate the surface area and volume of each shape.

2. CONTENTS
 CUBE
 CUBOID
 CYLINDER
 CONE
 SPHERE
 HEMISPHERE
 FRUSTUM

3. • An object which looks like solid box-shaped that has six
identical square faces.
• A cube has 6 equal and plane surfaces. All the faces of a cube
are square in shape.
• In a cube there are 6 plane surfaces. There are 8 vertices and
12 edges.
• Two adjoining plane – surfaces meet at an edge. There are 12
edges in a cube and all the 12 edges are equal in length.
These edges are straight edges.
• The meeting point of two edges is called a vertex. In a cube
there are 8 such vertices.

4. SURFACE AREA OF CUBE
TOTAL SURFACE AREA OF CUBE- 6(SIDE)²
LATERAL SURFACE AREA OF CUBE-
4(SIDE)²

5. VOLUME OF CUBE
VOLUME OF CUBE-
(SIDE)³

6. • The cuboid has 6 rectangular faces. The opposite
rectangular plane surfaces are identical (equal in all
respects). It has 8 vertices and 12 edges.
• In a cuboid there are 6 rectangular plane surfaces. There
are 8 vertices and 12 edges.
• A cube is also a cuboid having all its 6 faces equal and
square. Thus, a cube has all the six faces identical, whereas
a cuboid has the opposite faces identical.

7. SURFACE AREA OF CUBOID
TOTAL SURFACE AREA OF CUBOID =
2(lb+BH +lh)
LATERAL SURFACE OF CUBOID:
2(l+b)h

8. VOLUME OF CUBOID
VOLUME OF CUBOID –
L*B*H

9. • A cylinder stands on a circular plane surface having circular
plane surfaces on its top and bottom. Thus a cylinder has
two circular plane surfaces, one at its base and another at
its top. It has a curved surface in the middle.
• It has two edges, at which the two plane surfaces meet
with the curved surface. These edges are curved edges.
• In a cylinder there are 2 plane surfaces and 1 curved
surface. There are 2 edges and no vertices.
• The base and top of a cylinder are of the same shape
(circular) and size. Thus, both are identical.
• cylinder

10. SURFACE AREA OF CYLINDER
Curved surface area: 2Пrh
Total surface area: Пrh +2Пr2
=2ПR(H+R)

11. VOLUME OF CYLINDER
Volume of a cylinder: Пr2h

12. • A cone has one plane circular surface, i.e. its base and only
one curved surface. In a cone there is 1 plane surface and
1 curved surface. There are 1 edge and 1 vertex.
• It has one edge which is formed by the circular plane
surface meeting with the curved surface. The edge of a
cone is a curved edge.
CONE

13. SURFACE AREA OF CONE
TOTAL SURFACE AREA OF CONE-
∏R(L+R)
LATERAL SURFACE AREA OF CONE-
∏RL

14. VOLUME OF CONE
VOLUME OF CONE-1/3 Пr²h

15. SPHERE

16. • The ball-like shape is called a sphere.
• In sphere there is curve surface, no edge and no vertex.
• Some of the common solid figures are explained above in
brief with the labeled diagram to get the basic ideas of the
solid shapes.
SPHERE

17. SURFACE AREA OF SPHERE

18. VOLUME OF SPHERE

19. HEMISPHERE

20. SURFACE AREA OF
HEMISPHERE
TOTAL SURFACE AREA OF A HEMISPHERE:
3ПR2
CURVED SURFACE AREA OF A HEMISPHERE:
2ПR2

21. VOLUME OF HEMISPHERE
VOLUME OF A CUBE:
2/3 ПR 3

22. FRUSTUM

23. SURFACE AREA OF FRUSTUM
TOTAL SURFACE AREA OF A FRUSTUM:
П(R+R)L + ПR 2 + ПR 2
=П(R+R)L + П(R 2+ R2)
CURVED SURFACE AREA OF A FRUSTUM:
П(R+R)L

24. VOLUME OF FRUSTUM
VOLUME OF A FRUSTUM:
1/3 ПH(R 2+R 2+RR)