The document defines and provides formulas for calculating surface areas and volumes of various 3D shapes including cuboids, cubes, cylinders, cones, spheres, and hemispheres. It states that a cuboid is a 3D shape with right angles and equal opposite faces. The surface area of a cuboid is 2(length x breadth + breadth x height + height x length). The volume of a cuboid is length x breadth x height.

2. A cuboid is a 3-d shape in which
all angles are right angles, and
opposite faces are equal.

3. Lateral Surface area
The lateral surface area of a cuboid is
2h(l+b), i.e. ,2 x height x sum of length and
breadth
Surface area
The surface area of a cuboid is 2(lb+bh+hl) , i.e.
, 2 x (length x breadth + breadth x height +
height x length)

4. Volume of cuboid is lbh , i.e. , length x breadth x
height

5. A cube is a three-dimensional solid
object bounded by
six square faces, facets or sides, with
three meeting at each vertex. The cube
can also be called
a regular hexahedron and is one of the
five Platonic solids.

6. Lateral Surface area
The lateral surface area of cube is 4a2
Surface area
The surface area of cube is 6a2

7. Volume of cube is a2

8. 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.

9. Lateral surface area
The lateral surface area of cylinder is 2πrh
Surface area
The surface area of cylinder is 2πr(r+h)

10. Volume of cylinder is πr²h

11. A cone is a 3-dimensional geometric shape that
tapers smoothly from a base (usually flat and
circular) to a point called the apex or vertex.
In common usage in
elementary geometry, cones are assumed to
be right circular, where right means that the
axis passes through the centre of the base
(suitably defined) at right angles to its
plane, and circular means that the base is
a circle.

12. Lateral surface area
Lateral surface area of cone is πrl
Surface area
Surface area of cone is πr(l+r)

13. Volume of cone is 1/3 πr² h

14. A sphere is a perfectly round geometrical object
in three-dimensional space, such as the shape
of a round ball. Like a circle, which is in two
dimensions, a sphere is the set of points which
are all the same distance r from a given point in
space. This distance r is known as the radius of
the sphere, and the given point is known as
the center of the sphere. The maximum
straight distance through the sphere is known
as the diameter. It passes through the center
and is thus twice the radius.

15. Total surface area of sphere is 4πr²

16. The volume of a sphere is 4/3πr3

17. A sphere is divided into two equal "hemispheres"
by any plane that passes through its center. If
two intersecting planes pass through its
center, then they will subdivide the sphere into
four lunesor bi-angles, the vertices of which all
coincide with the antipodal points lying on the
line of intersection of the planes.

18. Curved surface area
The curved surface area of Hemisphere is 2πr2
Surface area
The total surface area of hemisphere is 3πr2

19. The volume of hemisphere is 2/3πr3