Transcript Cylchlythyr mesur Circular measure

Areas and Volume
Unit 4:Mathematics
Aims
•
Introduce standard formulae
to solve surface areas and
volumes of regular solids.
Objectives
Be able to use trigonometric
methods and standard formula to
determine areas and volumes.
2
Areas
There is 2 types of areas
 Cross Sectional Area
 Surface Areas
Petryal
Cross sectionalTriongl
Area
Sgwâr
Sector
Cylch
Annulus
Paralelogram
Area of Regular Hexagon = A =
* side2
A = 2.598 x Side2 (Approximately)
If the side length of regular hexagon is
6 meter, calculate the area of
regular hexagon using area formula?
Given:
Side length = 6 m.
Area of Regular Hexagon =
A = 2.598 x Side2
A = 2.598 x 62
A = 2.598 x 36
A = 93.53
Therefore, Area of Regular Hexagon
is 93.53 Square meter.
Area of parallelogram = 11 x 6
= 66cm²
Radius of circle = 4 / 2 =2cm
Area of circle = π x 2²
=12.56637cm²
Area of shape = 66 - 12.56637
=53.4cm²
Approximately how much aluminum is needed
to cover this soda can that has a radius of 2
inches and a height of 5 inches?
SA=2πrh+2πr2
SA= 2(3.14)(2)(5)+2(3.14)(2)(2)
SA= 62.8 +25.12
AA SA= 87.92 in.2 of aluminum
Volume
Volume
• The volume of every solid,
liquid or gas, is how much
three-dimensional space it
occupies, often quantified
numerically.
• Volumes of a number of simple
shapes, such as regular, straightedged, and circular shapes can
be easily calculated using
arithmetic formulas.
• More difficult shapes can be
calculated by integral calculus if
a formula exists for its
Rectangular prism
Find the volume of the
rectangular prism of sides
10cm, 15cm, 25cm.
Let,
a=10cm,b=15cm, c=25cm
Formula used: a x b x c
Solution:
Volume of the rectangular prism =
10 x 15 x 25
•
= 3750 m3
Sphere
Volume of a sphere =
4/3πr3
Find the volume of a
sphere of radius 9.6 m
Solution:
Volume of a sphere =
4/3πr3
= 4/3(3.14*9.63)
= 1.33(3.14*884.736)
= 1.33*2778.07104
Cylinder
Volume of a cylinder
= πr2h
Locate the volume of a
cylindrical canister with
radius 7 cm and
height 12 cm.
Solution:
Volume of a cylinder
= πr2h
= 3.14* 72*12
= 3.14*49*12
3
Triangular
Findprism
the volume of a triangular
prism whose length is 3cm,
base is 3cm and height is
3cm?
Solution:
Given: l = 3, b = 3, h = 3
Formula:
Volume of a triangular prism =
½ (lb)h
=½
(3×3)3
=½
(27)
=
13.5cm3
Square pyramid
Volume of Square
Pyramid = (1/3) b²h
Locate the surface area
and volume of a square
pyramid with the given
side 3, height 4 and the
slant height 5.
Solution:
Volume of Pyramid
= (1/3) b²h
= (1/3)* 3² * 4
= 0.33 * 9 * 4
= 12.
Cone
Volume = 1/3πr2h
Locate the volume of
cone whose base
radius is 2.1 cm and
height is 6cm using
π =22/7
Solution:
Volume = 1/3πr2h
= 1/3*22/7* 2.12*6
= 27.72 cm3
Volume = a³
Cube
Locate the volume,
surface area and
diagonal of a cube
with the given side 3.
Solution:
Volume = a³
= 3³
= 27.
Area and volume of hexagon
Volume of the hexagonal prism =
cross sectional area (csa) x
height(h).
If the side length of regular hexagon
is 8 cm and 3 meters high,
calculate the area and volume of
a regular hexagon?
Area and volume of hexagon
Side length = 8 cm.
Area of Regular
Hexagon =
A = (2.598) x Side2
A = 2.598 x 82
A = 2.598 x 64
A = 166.27cm²
Volume = csa x height = 166.27 x
300=49881cm³
How much paint will this paint can hold if it
is 8 inches in diameter and 12 inches in
height?
V= πr2h
V= 3.14(4)(4)(12)
V= 602.88 in.3 o baent
of paint