This document provides formulas and information about the surface areas and volumes of various geometric shapes including cuboids, cubes, cylinders, cones, spheres, hemispheres and frustums. It defines each shape and provides their respective formulas to calculate total surface area, curved surface area and volume. Formulas are given for cuboid, cube, cylinder, cone, sphere, hemisphere and frustum. Additional details are provided on cylinders, cones, spheres and the related terms quadrant, sector, segment and the differences between minor and major sectors and segments.

2. Topics covered:-
Formulas
Information on:-
o Cuboid
o Cube
o Cylinder
o Cone
o Sphere

3. Shape Total surface
area
Curved
(Lateral)surfa
ce area
Volume Longest
Diagonal
Cuboid 2(lb+bh+hl) 2h(l+b) lbh
Cube 6a2 4a2 a3 a√3
Cylinder 2πr(r + h) 2πrh πr2h
Hollow Cylinder π(R2- r2) 2πh(R+r) πh(R2-r2)
Cone πr[r + √(r2 + h2)] πr√(r2 + h2) 1/3πr2h
Sphere 4πr2 4πr2 4/3 πr3
Hemisphere 3πr2 2πr2 (2/3)πr3
Frustum π[ r1
2 + r2
2 + (r1 *
r2) * √[(r1 - r2)2 +
2
π(r1 + r2)√[(r1 -
r2)2 + h2]
(1/3)πh [r1
2 +
r2
2 + (r1 * r2)]
Formulae

4. Cuboid
 A cuboid is a convex
polyhedron bounded by
six quadrilateral faces.

5. Cube
A cube is a three-dimensional solid object bounded by
six square faces, facets or sides, with three meeting
at each vertex.
The cube is also a square parallelepiped, an
equilateral cuboid and a right rhombohedron. It is a
regular square prism in three orientations, and a
trigonal trapezohedron in four orientations.

6. Cylinder
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. The surface area and
the volume of a
cylinder have been known since deep antiquity.
A cylinder whose cross section is an ellipse, parabola,
or hyperbola is called an elliptic cylinder, parabolic

7. Cone
 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.
 More precisely, it is the solid figure bounded by a base in
a plane and by a surface (called the lateral surface)
formed by the locus of all straight line segments joining
the apex to the perimeter of the base, such that there is
a circular cross section. The term "cone" sometimes
refers just to the surface of this solid figure, or just to the
lateral surface.

8. A sphere is a perfectly round geometrical object in three-
dimensional space.
Like a circle a sphere is defined ,mathematically, as the set of
points that are all the same distance r from a given point in
three-dimensional space.
This distance r is the radius of the sphere, and the given point is
the center of the sphere.
The maximum straight distance through the sphere passes
through the center and is thus twice the radius; it is
the diameter.

10. Circumference= 2πr
Area= πr2
Area of semi-circle= πr2/2
Area of quadrant of a circle= πr2/4
Area of a sector of a circle= πr2θ/360

11. Quadrant
 A quarter of a circle made by two radiuses at
right angles and the connecting arc is known as
Quadrant.

12. Sector of a circle
A circular
sector or sector of a
circle(symbol: ⌔), is
the portion of
a disk enclosed by
two radii and an arc.

13. Sector
Minor
sector
Major
sector
Major sector
Minor sector

14. Difference between a minor sector
and a major sector
Minor sector
 The smaller portion
of a circle that is
cut off by 2 radii of
a circle, is known
as Minor Sector.
Major sector
 The larger portion
of a circle that is
cut off by 2 radii of
a circle, is known
as Major Sector.

15. SEGMENT
In geometry, a circular
segment (symbol: ⌓) is
an area of
a circle informally defined
as an area which is "cut
off" from the rest of the
circle by a secant or
a chord.
Segment
Minor
segment
Major
segment

16. Difference between a minor segment
and a major segment
Minor segment
 The smaller portion of a
circle that is cut off by a
chord is known as minor
segment.
Major segment
 The larger portion of a
circle that is cut off by a
chord is known as major
segment.

17. Difference between a quadrant and a
sector
Quadrant Sector
 A quarter of a circle made
by two radiuses at
right angles and the
connecting arc is known as
Quadrant.
 A circular
sector or sector of a
circle(symbol: ⌔), is the
portion of a disk enclosed
by two radii and an arc.

18. Efforts by- Arpan Goyal(X th a)
SUBMITTED TO- RAJENDER SIR