intervention material
TRANSCRIPT
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Republic of the Philippines
DEPARTMENT OF EDUCATION
Region IV-A CALABARZON
Division of Batangas
BAUAN NATIONAL AGRICULTURAL AND VOCATIONAL HIGH SCHOOL
San Agustin,Bauan,Batangas
INTERVENTION MATERIAL
Prepared by:
LINA C. BEJER
Math III Teacher
GABRIEL R. ROCO
Principal III
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MODULE IN MATHEMATICS
SURFACE AREA
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INTRODUCTION
Hey! Im your friend in Math. You can call me
Supermath if you want. Im just an ordinary person butthey used to call me Supermath because I have the
patience to solve it all. Cmon its easy, all you need is
patience. Just remember that patience is a virtue. Im
sure you will be good too in Math. Want to bet?
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To the Readers,
This module entitled Surface Area is careful made for you. It
tackles how to solve the surface areas of some solids step by
step to understand the lesson well.it is important that at your
age, you already competent with this lesson
I have prepared varied exercise for you to master and apply
the skills that you have learned
The Author
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OBJECTIVES
After reading this module, you should be able to:
a. To know what is surface area
b. Solve for the surface area of some solidsc. Solve problems involving surface area
d. Manifest self-confidence
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DISCUSSION
Surface Area
Surface Area is defined as the sum of the areasof the outer surfaces of a solid. These outer
surfaces are known as faces.
Having studied polygons and their areas, as well
as polyhedrons and their characteristics, it will beeasy to understand how the total area of the
surfaces of solids is obtained.
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Surface Area of a Cube
To find the surfaces area of a cube,multiply the square of the length of
side by 6.
Theorem
The surface area (SA) of a cube side (s) is given by:SA= 6s
2
SIDE
LATERAL FACE
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Example:Find the surface area of a cube with a side
of length 6cm.Solution:Using the formula for the surface area of a
cube, SA= 6s2
, we have
SA = 6s2
=6(6cm)2
= 6(36cm2)
SA = 246cm2
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Surface Area of a Rectangular Prism
To find the surface are
(SA) of a rectangular
prism, add the areas of its
faces.
Theorem
The surface area (SA) of a rectangular prism of length(I), width (W), and height (h) is given by:
SA = 2hw + 2lw + 2hl
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Example:Find the surfaces area of a rectangular
prism whose length is 7cm, width is 4 cm, and heightis 5 cm.
Solution:Using the formula for the surface area
of rectangular prism, SA = 2lw + 2hw + 2hl, we have
SA = 2lw + 2hw + 2hl
SA = 2(7cm) (4cm) + 2(5cm) (4cm) + 2(5cm)(7cm)
= 56 cm2+40 cm2+70cm2=166 cm
2
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Surface Area of a Right Square Pyramid
To find the Surface Area
of a right square pyramid,
add the area of the square
base and the areas of thefour triangular faces
Theorem
The surface area of a right square pyramid with a
base of side (s) and a slant height () is given by
SA = S2+ 4 (
) or SA = s
2+ 2 (s x )
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Example:Find the surface area of the right square
pyramid with base of side 3cm and slant height of 5cm.
Solution:Using the formula for the surface area of a
right square pyramid, SAS2
+2(S x ), we have
SA = S2+2(S x )
SA = (3cm)2+ 2[(3cm) x (5cm)]
=9cm2+2(15 cm2)=9cm
2+30cm
2
SA=39cm2
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Surface Area of a Circular Cylinder
To find the surface area of a right
circular cylinder, add the areas of
the circular bases and the area of
the rectangular region which isthe body of the cylinder.
Theorem
The surface area (SA) of a right circular
cylinder of radius (r) and height (h) is given by:
SA + or SA =
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Example:Find the surface area of a right circular
cylinder which has height and 20cm and a base
radius of 5cm.
Solution:Using the formula for the surface area of a
right circular cylinder, SA = 2 , we have
SA = 2
SA =2(5 cm)(5 cm + 20 cm)SA = 2(5 cm)(25 cm)
SA = 2(125 cm2)
SA= 250 cm2
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Surface Area of a Right Circular Cone
To find the surface area of a
right circular cone, add the areas of
the base which is a circle (), and
the curved surface which is thelateral area (r).
Theorem
The surface area (SA) of a right circular cone of radius
(r) and slant height () is given by SA= + r
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Example:find the surface area of a circular cone if
the radius of its base is 3.5cm and its slant height is7.25cm.
Solution:Using the formula for the surface area of a
right circular cone, SA=
+ r, we have
SA= + r
SA= (3.5 cm)2+ (3.5 cm)(7.25 cm)
SA= (12.25 cm2) + (25.375 cm2)SA= 12.25cm
2+ 25.375 cm
2
SA= 37.625cm2
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Surface Area of a Sphere
Recall that a sphere is the set of
all points in space equidistant
from a fixed point called center.
The fixed distance is called theradiusof a sphere.
Theorem
The surface area (SA) of a sphere of radius (r) is given by
SA= 4
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Example: What is the surface area of a ball with a
radius of 6cm?
Solution: Using the formula for the surface area of a
sphere, SA= 4, we have
SA = 4
SA = 4(6 cm)2
SA= 4(36 cm)2
SA= 144cm2
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Practice
SOLVING SURFACE AREAS
1. Find the surface area of a cube whose side is 4cm.
2. Find the surface area of a cylinder whose diameter of
base is 6cm and have a height of 10cm.
3. Find the surface of a rectangular prism with a length
of 6cm, a width of 3cm and a height of 2cm.
4.
A cone has a slant height of 13 cm and the radius of
the base is 6.25 cm. Find the surface area of the cone.
5. A ball has a radius of 6 cm, find its surface area.
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Exercises:1.
A cylindrical tank is 2.6 meters high. If the radius of its base is 0.92
meter, what is the surface area?
2.If a cube with a side of 2.2 cm needs a wrapper for its cover, how
many centimeters of wrapper is needed to cover the cube?
3.
Theres a cone with a radius of 5 cm and a slant height of 12 cm.
your teacher asked you to find the surface area, what will be youranswer?
4.
The third year students are constructing a square pyramid for their
project. They plan to cover it with a manila paper. If the side of the
base of the pyramid measures 2.2 meters and the height of each
triangular face is 1.6 meters. What size of manila paper will beneeded to cover the square pyramid?
5.
Jasper has a ball whose surface area is 314 cm2. He wants to know
the radius of his ball, what should be his answer?
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6.A metal tube is in the form of right circular cylinder. The radius of its
base is 4 cm and its height is 10 cm. Find the surface area of the
metal tube.7.
Find the surface area of a rectangular box with a length of 2.1 cm, a
width of 2.7 cm and a height of 3 cm.
8.A cube has a surface area of 294 cm2, what is the measure of its
side?
9.
The diameter of a spherical tank is 1.4 m. What is the surface area?10.
A refrigerator is 5.008 square meters. If its length is 0.8 meter
and its width is 0.51, what is its height?
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Keep Your Skill Sharp
Solve the following:
1.
How many square centimeters of gift wrapper is
needed to wrap a box 9cm by 15 cm by 7 cm allowing 4
cm2 for folding and pasting?
2.
Find the edge of a cube it its surface area is 384square meters?
3. Find the surface area of a square pyramid if the slant
height is 16.5 cm and a side of the base is 8 cm.
4.
Find the lateral area of a cone whose radius is 3 cmand a slant height of 5 cm.
5. What is the surface area of a marble whose diameter
is 10 millimeters?
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6. Find the surface area of a ball with a radius of 9.7
millimeters.
7.
Find the surface area of a right circular cylinder if it is
40 mm high and the radius of its base measures 10.2 mm.
8. The base edge of a square pyramid has a length of 3
dm. If each lateral face has an area of 12 dm2, what is the
total surface area of the pyramid?9. The edge of the cube measures 7.5 cm. What is the
surface area?
10.
Find the surface area of a globe, which is 6 cm in
diameter.
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Great!!! You have finished this module. Now check your answers in
Practice Solving Surface Areas, Exercises and Keeping your Skill
Sharp.Practice Solving Surface Areas
1. 96 cm2
2.
3.
4. 120.3125
5. 144
Exercises
1. 6.4768
2. 29.04
3. 266.9
4. 11.88
5. 5
6. 112
7. 40.14
8.
7 9. 1.96
10.1.6
Keeping Your Skill Sharp
1. 606 cm2
2. 8 m
3. 64 cm2
4. 24
5. 100
6. 376.36
7. 1024.08
8. 432
9. 337.5
10.36 c
Goodbye!!!
See you in the next module!
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