Quarter 4-Week1-MATHEMATICS-5.power point presentation

MATHEMATICS 5
QUARTER 4 WEEK 1
D
A
Y
1
Finding the Area of a Given
Circle

Activity: Identify the following objects:
What did you notice on the
given pictures?

Let us recall how to find the
circumference of a circle.
The distance around a circle is called
its circumference.
The distance across a circle through its
center is called its diameter.

We use the Greek letter (read as “Pī”
with a short i) to represent the ratio of
the circumference of a circle to its
diameter. When rounded off, = 3.14.

In this lesson, you are going to derive
the formula for area of a circle. Do
you know that finding the area of a
circle is easier if we use a formula?
Let’s Find it out.

Areas have many practical
applications even in the past
centuries.
• The Chinese knew how to calculate
the area of many different two-
dimensional shapes by about 100 B.C.

• Johannes Keppler, 1571 to 1630, measured the
areas of sections of planetary orbits using
formulas for calculating areas of ovals or circles.
• Sir Isaac Newton used the concept of area to
develop Calculus.
The concept of area became even more useful
when formulas in finding areas of different shapes
were developed.

The area of a circle is the total region
that is bounded by the
circumference.
Think of the area of a circle as the
amount of surface enclosed inside the
circle.

The formula in finding the area of a
circle is:
𝐴=𝜋 𝑟2
𝑜𝑟 𝐴=𝜋 𝑥 𝑟 𝑥 𝑟
In this formula, "A," is the area, "r" is the
radius, and “” is a Greek letter pronounced
as "pi" which is constant and approximately
equal to 3.14, the ratio of the circumference
to its diameter.

Recall that the radius (r) of a circle is the distance
from its center to any point on the circle.
Example 1 : The radius of a circle is 3 meters. What is
the area of the circle?
Solution: 𝐴=𝜋 𝑟2
𝐴=(3.14)(3 𝑚)2
𝐴=(3.14)(3𝑚)(3𝑚)
𝐴=(3.14)(9 𝑚2
)
𝐴=28.26 𝑚2

Example 2:
The diameter of a circle is 8 centimeters. What is the
area of the circle?
Solution:
𝐴=𝜋 𝑟2
𝐴=(3.14)(4 𝑐𝑚)2
𝐴=(3.14)(4 𝑐𝑚)(4 𝑐𝑚)
𝐴=(3.14)(16 𝑐𝑚2
)
𝐴=50. 24 𝑐𝑚2
Find first the
radius:
d = 2 x r
8 cm = 2 x r
8cm ÷ 2 = r
r= 4 cm

You Complete Me!
Directions: In the diagram, the circle has a radius
of 6 cm. Find the area of the circle by filling out
the blanks to complete the solution. Write your
answer on a separate sheet of paper.

Consider the situation below!
Mr. Suarez is purchasing
materials to build a do-
it-yourself trampoline
for his kids. If he wants
the diameter of the
mat to be 14 feet long,
how much nylon does
he need to purchase?
If the diameter is 14
ft, what is the
radius?
R = 7ft

Consider the figure below!
The red line through
the center of this
trampoline shows its
diameter and can be
used to calculate its
area.
𝐴=𝜋 𝑟2
𝐴=(3.14)(7 𝑓𝑡)2
𝐴=(3.14)(7 𝑓𝑡)(7 𝑓𝑡)
𝐴=(3.14)(49 𝑓𝑡2
)
𝐴=153.86 𝑓𝑡2

What is the formula in
getting the area of a
circle?
What’s the first thing to do
if diameter is given to find
the area of a circle?

Can You Measure Me?
Directions: Answer the following questions. Show
your solutions. Write your answer on a separate
sheet of paper.
1. The radius of a circle is 9 centimeters. What is
2. The diameter of a circle is 12 meters. What is
3. The radius of a circular rug is 4 feet. What is
the area of the rug?

MATHEMATICS 5
QUARTER 4 WEEK 1
D
A
Y
2
Area of a Given Circle

Lets Review!
Directions: In the diagram, the circle has a radius
of 6 cm. Find the area of the circle by filling out
the blanks to complete the solution. Write your
answer on a separate sheet of paper.
r
3.14 6
36
113.04

Are you familiar with the object below?
Do you know how to tell the
time?
Why is it important to know the
time?
The clock tells us the correct
time. The small hand of the
clock tells the hour while the
long hand tells the minute.

If the shorthand
measures 2.2 cm and
the long hand is 4.7
cm. What is the area
of the circle using the
long hand of the
clock as the radius?

Try to answer the following questions:
1. What is asked?
The area of the clock.
2. What are the given?
2.2. cm and 4.7 cm
3. How do we find the area of the circle?
4. What is the formula in finding the area
of a circle?

Take note that in finding the area of a circle,
we use the formula:
Where: = 3.1416. or 3.14 and r = radius
let’s apply the formula in solving the problem
above.
π = 3.14.
r = 4.7 cm - the measurement of the long hand

let’s apply the
formula in solving
the problem
above.
π = 3.14.
r = 4.7 cm - the
measurement of
the long hand
𝐴=𝜋 𝑟2
𝐴=(3.14)(4.7 𝑐𝑚)2
𝐴=(3.14)(4.7 𝑐𝑚)(4.7𝑐𝑚)
𝐴=(3.14)(22.09 𝑐𝑚2
)
𝐴=69.3626 𝑐𝑚2

Let’s have
another example:
The radius of a
circle is 3 inches.
What is the area
of the circle?
r = 3 in
𝐴=𝜋 𝑟2
𝐴=(3.14)(3 𝑖𝑛)2
𝐴=(3.14)(3𝑖𝑛)(3𝑖𝑛)
𝐴=(3.14)(9 𝑖𝑛2
)
𝐴=28.26 𝑖𝑛2

Let’s have
another example:
The area of a
circle is 78.5
square meters.
What is the radius
of the circle?
𝐴=𝜋 𝑟2
78.5 𝑚
2
=(3.14 )𝑟
2
78.5 𝑚
2
=(3.14 ) 𝑟
2
3.14 3.14
2 5 𝑚2
=𝑟 2
2 5 𝑚2
=𝑟 2
√ √
5𝑚=𝑟

Find the area of the circle to the nearest
tenths. Use 3.14 for π. (Remember to
include the square units in your answer).
1. radius - 7 cm
Area _________________________________
2. radius - 12 in.
Area - _________________________________
3. diameter - 18 mm
Area - _________________________________
153.86 𝑐𝑚2
452.16 𝑖𝑛2
254.34 𝑚𝑚2

Remember:
The area of a circle is the number of
square units inside the circle. It has the
formula;
A = or A = x r x r
Take note also that Pi is the ratio of the
circumference of a circle to its
diameter, Pi is always the same number
for any circle.

The value of π (pi) is approximately
3.1416 but usually rounded to 3.14.
since the formula is only given in
terms of radius, remember to
change from diameter to radius
when necessary.
The radius is always equal to half of
the diameter.

MATHEMATICS 5
QUARTER 4 WEEK 1
D
A
Y
3
Solving routine problems
involving area of a circle.

Find the area of the circle to the nearest
tenths. Use 3.14 for π. (Remember to
include the square units in your answer).
1. radius - 7 cm
Area _________________________________
2. radius - 12 in.
Area - _________________________________
3. diameter - 18 mm
Area - _________________________________
153.86 𝑐𝑚2
452.16 𝑖𝑛2
254.34 𝑚𝑚2
Review!

What do you mean by the word Routine?
• Routine problems are real life problems.
- It involves at least one of the four
operations to solve practical problems.
- It requires basic skills and an organized and
sequenced step.
- Planned strategies and methods are
needed to come up with the answer.

Read and understand the problem below.
Aling Belen has a circular garden. Even before
the Pandemic, she had planted it with different
kinds of vegetables with the help of her 5
children. Every harvest she shares them with her
less fortunate neighbors and sells the rest. Her
garden with a diameter of 20 meters yields more
fruits. Can you find the area of Aling Belen’s
garden?

There are Four-Step Method to solve the
problem.
UNDERSTA
ND
PLAN
SOLVE CHECK
Know what is asked.
Identify the given.
Choose the
operation or formula
Perform Strategy Verify if the answer is
correct.

Suggested Strategies
a. Drawing a model/diagram
b. Using a formula and changing
them to mathematical symbol.
c. Working Backward

• The area of a circle is the number of
square units inside that circle.
• The formula in finding the area of a circle
(A = π)
To solve the problem, we can use the 4-step
method.

Understand
 Know what is asked.
The area of Aling Belen’s garden
 Know the given facts.
20 meters – diameter of the garden

Plan
 Determine the operation or formula to
be used.
Formula: (A = πr2)
Operation: Multiplication

Solve
 Use and change the formula
into mathematical sentence.
 (A = πr2)
 Substituting the formula:
where π = 3.14
r = 20m/2= 10m
A = 3.14 x 10m x 10m
A= 314 - the area of Aling Belen’s circular
garden

Check:
To check if you solved the problem
correctly. You can solve for either the
radius or the pi. This time we are going
to solve for the pi by dividing the area
by the radius.

Let us try another example.
Aling Belen bought a circular rag
for the front door to keep the
house clean. The rag that she
chose has a radius of 12
centimeter. What is the area of
the rag?

Understand;
 Know what is asked or the unknown.
The area of the rag.
 Know the given facts.
12 cm - radius.

Plan:
Determine the operation or formula to
be used.
 Formula: (A = π)
Operation: Multiplication

Solve:
Show how the solution is done.
 Use and change the formula into
mathematical sentence.
(A = πr2)
 Substituting the formula:
where π = 3.14
r = 12 cm
A = 3.14 x 12 cm x 12cm
A= 452.16 cm2- the area of the rag

Check:
To check if you solve the problem correctly
you can solve for either the radius or the pi.
This time we are going to solve for the pi by
dividing the area by the radius.

Your Turn!
A garden has four identical circular
plots in each corner. If each plot has a
radius of 8 ft, what is the area of all the
plots?

Let’s Apply!
Samantha’s mother love to bake cake.
She went to the market to buy a cake
board. She bought the board with a
diameter of 3 cm. Find the area of the
board.

REMEMBER:
Routine problems are practical problems and
can be solved using the 4-step method. These
methods are:
1. understanding the problem - know what is
asked and identify the given facts
2. planning - determine the formula or operation
that you are going to use
3. solving - show how the solution is done
4. checking

Direction:
Choose the letter of the correct answer.
1. Mother made a circular plot with 15 ft in
diameter. Find the area of mother’s plot?
A) 178.625
B) 177.625
C) 176.625
D) 176

Direction:
2. What is the area of a circle with the
diameter of 18 centimeters?
A) 254.34 cm2
B) 253.34 cm2
C) 154.34 cm2
D) 153 cm2

Direction:
3. Candice made a pancake with the
radius of 5 cm. What is the area of the
pancake?
A) 88.5 cm2
B) 78.5cm2
C) 68.5cm2
D) 58.5cm2

Direction:
4. Mian loves her pet cats so she bought a
soft rag with a radius of 25cm as their bed.
Find the area of the rag.
A) 490.625 cm2
B) 625 cm2
C) 1962.5 cm2
D) 1963.5 cm2

Direction:
5. John’s favorite plate has a diameter of
13mm. What is the area of the plate?
A) 132
B) B) 132.665
C) 133.665
D) 232.665

MATHEMATICS 5
QUARTER 4 WEEK 1
D
A
Y
4
Solving non-routine
problems involving area of
a circle.

Review:
What are the Four-Step Method in solving
the problem.
1. Understand: Know what is asked.
Identify the given facts.
2. Plan: Choose the operation or the formula
to be used.
3. Solve: Perform the strategy.
4. Check: Verify if the answer is correct.

A non-routine problem is any complex
problem that requires some degree of
creativity or originality to solve. Non-routine
problems typically do not have an
immediately apparent strategy for solving
them. Oftentimes, these problems can be
solved in multiple ways.

Read and understand the problem below.
A square garden has an area of 25 sq. m. A
sprinkler at a center of the garden covers
the side of the garden. What is the area
cover by the sprinkler?

Applying the four steps in solving non-
routine problems;
1. Understand: Know what is asked.
Identify the given facts.
2. Plan: Choose the operation or the
formula to be used.
4. Check: Verify if the answer is correct.

Going back to the problems, the answers
follow;
1. Understand: Know what is asked. Identify
the given facts.
What is asked in the problem?
The area covered by the sprinkler.
What is the needed information to answer
what is asked for?
25 area of the garden

2. Plan: Choose the operation or the
formula to be used.
Now it’s time to decide on a plan of
action! Choose a reasonable problem
-solving strategy. Several are listed
below. You may only need to use one
strategy or a combination of
strategies.

• draw a picture or diagram
• make an organized list
• make a table
• solve a simpler related problem
• find a pattern
• guess and check
• act out a problem
• work backward

In our problem what we will do is to
draw a diagram.
The given is only the area of the
square garden and what is asked
for is the area of the circle. We
have to find first the measurement
of the side of the square from its
area to know the diameter of the
circle. From its diameter we can
get the radius and solve for the
area of the circle.

Area of a square = side x side
25 sq. m = s x s
25 sq.m = 5m x 5m
Side = 5m

Now it’s time to dig in and get to
work!
If the side of the square is 5m, the
diameter of the circle is also 5m.
R= half of diameter therefore, r= 2.5 m

To solve for the area of the circle we
use the formula;
A=
A = π x r x r
= 3.14 x 2.5m x 2.5m
= 3.14 x 6.25 m2
A= 19.625 m2

4. Check:
Verify if the answer is correct.
You’ve come so far, but you’re not
finished yet! A mathematician must
always go back and check his/her
work. Reviewing your work is just as
important as the first 3 steps!

Before asking yourself the questions
below, reread the problem and
review all your work.
Therefore, the area covered by the
sprinkler is 19.625 sq. m

Let’s try another one.
Bernadette has a circular fountain. In the
middle of the fountain there is a statue with
a diameter of 2m. The diameter of the
fountain is 10m. What is the area of the
fountain not covered by the statue?

What is asked:
The area of the fountain not covered by the
statue
What are the given:
Diameter of the fountain = 10m
Diameter of the statue = 2m

What to do?
Make a drawing. The colored circle is the
statue and we are going to find the area of
unshaded part.

Find the area of the fountain and statue then
subtract.
Area of the fountain
A = π x r x r
= 3.14 x 5m x 5m
= 3.14 x 25
A= 78.5
78.5 m2 – 3.14 m2 = 75.36
Therefore, the area of the fountain without
the statue is 75.36
Area of the statue
A = π x r x r
= 3.14 x 1m x 1m
= 3.14 x 1
A= 3.14

Read the problem and do the needed steps.
A horse is tied with a rope in the center of
grassland to graze. The length of the rope is 5m.
The diameter of the circular grassland is is 50m.
find the area in which the horse cannot graze.
1.What is asked?
____________________________________________
2. What are the given?
____________________________________________

3. What strategy will you do?
______________________________________
4. What is the operation involve to solve
the problem?
_______________________________________
5. What is the answer?
_______________________________________

Jajan has a circular carpet in his drawing
room. He wants to put a circular table in the
middle of the carpet. The diameter of the
carpet is 12m and the diameter of the table
is 4m. how much area of the carpet is left
after putting the table in place?

REMEMBER
In solving non routine problems we can
used different strategies to be able to
it. You may only need to use one
strategy or a combination of strategies.
• draw a picture or diagram
• make an organized list
• make a table
• solve a simpler related problem

• find a pattern
• guess and check
• act out a problem
• work backward
• write an equation
• use manipulatives
• break it into parts
• use logical reasoning

Read the problem then choose the letter
of the correct answer.
1. A circular mirror has 5cm frame around
it. The mirror itself is 20cm in diameter.
What is the area of the frame?
A. 4.71
B. 47.1
C. 471
D. 4710

2. Three identical coins are lined up in a
row. The distance between the center of
the first and third coin is 8 cm. What is the
area covered by the three coins?
A. 12.56
B. B. 21.56
C. C. 25.16
D. D. 26.51

3. A rectangular plaza has a surrounding
circular fence. The diagonals 60 meters long
of the rectangular pass from one point on
the fence through the center of the circle to
another point on the fence. What is the area
of the plaza including the fence?
A. 2286
B. B. 2682
C. 2628
D. 2826

4. find the area of the washer with
inner radius of 3cm and the outer
radius of 5 cm?
A.50.24
B. 50.42
C.52.40
D.54.20

5. The rectangle has an area of 20
sq.dm what is the area of the largest
circle that can be cut from it?
A. 56.12
B. 52.61
C. 12.56
D. 12.15

MATHEMATICS 5
QUARTER 4 WEEK 1
D
A
Y
5
Catch-Up Friday

Quarter 4-Week1-MATHEMATICS-5.power point presentation

More Related Content

Similar to Quarter 4-Week1-MATHEMATICS-5.power point presentation

More from GirlieTrinidad1

Recently uploaded

Quarter 4-Week1-MATHEMATICS-5.power point presentation