This document provides examples and explanations of math concepts related to surface area and volume. It includes two worked problems calculating the surface area of shapes defined by equations. The first problem calculates the surface area of part of a cylinder projected onto a rectangle, and the second problem calculates the surface area under a paraboloid. Formulas and steps are provided for the working of each problem.

1. LUAS
PERMUKAAN
Dosen Pengampu:
Agung Prasetyo Abadi, M.Pd
Kelompok
12

2. Autri Sekar
Kinanti
012110631050111
Naufal Dzaky
02 Varied exercises for ki
Anggota

3. Contoh Soal 1
Jika S daerah persegi panjang dibidang-xy
yang dibatasi oleh garis x = 0 , x = 1 , y = 0 , y
= 2. carilah luas sebagian dari permukaan
tabung z= 4 − 𝑥2 yang terproyeksikan ke
dalam S.
Penyelesaian:
Misalkan 𝑓 𝑥, 𝑦 = 4 − 𝑥2 . Maka 𝑓𝑥 =
−𝑥
4−𝑥2
,𝑓𝑦 = 0
Jadi luas permukaan G adalah

5. Contoh Soal
2
Carilah luas permukaan 𝑧 = 𝑥2 + 𝑦2 dibawah bidang
𝑧 = 9
Penyelesaian:
Misalkan 𝑓 𝑥, 𝑦 = 𝑥2 + 𝑦2. Maka 𝑓𝑥 = 2𝑥 , 𝑓𝑦 = 2𝑦
substitusi 4r2 + 1 = u
8r dr = du
r dr =
𝑑𝑢
8
jika r = 0 , u = 1
r = 3 , u = 37

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9. KINDERGAR
TEN
01
Exercises for junior and senior kindergarten

10. Write Your Answer Here Write Your Answer Here
I think… it started with an “s” and
it ended with an “n”!
I am pretty sure it started with an
“f” and finished with an “r”
Let’s count some more! Do you remember the numbers?
WHAT IS THIS TOPIC ABOUT? MATH, OF
COURSE!
? ? ? ? ? ? ? ? ? ? ?

11. Seven Fluffy Sheep’s
Tails
Four Juicy Apples
I think… it started with an “s” and
it ended with an “n”!
I am pretty sure it started with an
“f” and finished with an “r”
Let’s count some more! Do you remember the numbers?
WHAT IS THIS TOPIC ABOUT? MATH, OF
COURSE!
1 2 3 4 5 6 7 1 2 3 4

12. —Someone Famous
“It takes a big
heart to help
shape little
minds”

13. FEATURES OF THE TOPIC: NUMBERS
FROM 1-3
? Bear
This is easy! It’s the first!
? Elephants
Now, what’s next?
? Sheep
Hooray! You’ve made it!

14. FEATURES OF THE TOPIC: NUMBERS
FROM 1-3
ONE Bear
This is easy! It’s the first!
TWO Elephants
Now, what’s next?
THREE Sheep
Hooray! You’ve made it!

15. OVERVIEW DIAGRAM: STEPS FOR
PROBLEM-SOLVING
What Is The Question? Draw
Ana has 5 lions and wants to share them with
4 other friends. How many lions does each
person get?
Answer Explain
1 lion per person!
Ana and her friends make 5 people in total.
Since there are 5 lions, each gets 1 lion.

16. HOORAY
!
LEVEL UP!

17. PRIMARY
LEVEL
02
Varied exercises for kids from grades 1 to 3

18. INTRODUCING EXERCISES
In this section you will see basic
math operations and mathematical
test preparation. Also, we will
provide you with key words for
problem solving regarding addition,
subtraction, multiplication and
division. Lastly, you will find an
anchor chart for a mathematical
journal

19. Color the squares with the paint bucket tool! Feel free to make your exercise with the tables
DEFINITION OF CONCEPTS
Addition
6+4 = 10
Subtraction
10-6 = 4
Multiplication
2x4 = 8
Division
4÷2 = 2

20. 24x2=4
8!
How well are you on multiplications? Let’s practice!

21. PROCESS: CUT OUT THIS EXERCISE!
Jane has 10 owls. She wants to share with 3 of her friends. How many owls will each friend
get?

22. JUNIOR
03
Varied exercises for kids from grades 1 to 3

23. Answer
Here
Is the pyramid’s volume formula
Answer
Here
Is the cylinder’s volume formula
Answer
Here
Is the cube’s volume formula

24. V=(lwh)÷3
Is the pyramid’s volume formula
V=πr2h
Is the cylinder’s volume formula
V=lxbxh
Is the cube’s volume formula

25. PRACTICAL USES OF THIS SUBJECT: MATH
TOOLS
1
Calculator
Full of buttons
and all of the
numbers
2 Rulers
Ideal for straight
lines and sizes
35 Sheets
A tool for writing
math formulas
1
Compass
Handy for circle-
making

26. IT’S TIME
TO
LEARN!
How well are you on problem solving? Getting there?

27. PROBLEM VS SOLUTION
1. Problem
Read it thoroughly!
2. Strategy
Find your best shot for
it!
3. Find a Solution
Don’t give up even if you can’t find it at first!

28. PROBLEM VS SOLUTION
1. Problem
José is 3x older than
Aisa but -2x than Luis.
In total, they are 45y
2. Strategy
Find your best shot for
it!
3. Find a Solution
You can leave your logical reason below

29. SENIOR
04 Varied exercises for kids from grades 1 to
3

30. FROM
BASICS TO
PRO: LET’S
SOLVE THIS!

31. DID YOU KNOW THIS? MATH FOR PROS!
Write your answer
A number x is a number y
such that y2 = x
Write your answer
The statement x∈A means
that x is an element of A
Write your answer
The mathematical
constant e is
approximately to 2
Write your answer
Is used to indicate the
qualities of approximation
Write your answer
They are not of the same
quantity, quality, value, etc
Write your answer
Can be used to compare
numbers and expressions

32. DID YOU KNOW THIS? MATH FOR PROS!
Square Root
A number x is a number y
such that y2 = x
Is An Element Of
The statement x∈A means
that x is an element of A
Is Approximately
Equal
The mathematical
constant e is
approximately to 2
Plus-Minus Sign
Is used to indicate the
qualities of approximation
Is Not Equal To
They are not of the same
quantity, quality, value, etc
Is Greater Than Or
Equal
Can be used to compare
numbers and expressions

33. EXERCISE: ELECTRIFYING EXPONENTS
Fill the empty boxes with the correct answer. Remember to check what you write!!
Fill the empty boxes with the correct answer. Remember to check what you write!!
1)
4)
3)
2)
2 2
2
32
72
2
2
52
53
3 - ?
? - 5
9 - ?
?
?
?
?
?

34. STEPS FOR PROBLEM SOLVING IN THE
WORLD
Step #01
Finding the problem
and understanding it
Step #02
Strategize and find
the best way to solve
it
Step #04
Explain your answer
with a short text
Step #05
Hand it over to your
teacher and wait
Step #03
Find a solution and be
sure of it!
Hooray!
That’s All!

35. STEPS FOR PROBLEM SOLVING IN THE
WORLD
Guatemal
a
Americas
Madagasc
ar
Africa
Denmark
Europe
India
Asia
Russia
Europe - Asia
Australia
Australia

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37. Graphs may be hard but you can do it! Luckily, with Slidesgo, everything is easier for
you!
Perseverance is the biggest strength: you may not achieve it at first but you will, soon
Always strategize first before starting something
Understand the problem: it’s the key to everything
You can find the right solution! You just have to use your brain and what you’ve learned
To Remember
LIST: LET’S HELP YOU OUT!
Trust yourself: You’ll know you can! I surely do!

38. ASSIGNMENT: MAKE A GRAPH OF YOUR
PROGRESS
To modify this graph, click on it and follow the link
January February March April Today
0
100
75
50
25
?
93
%
68
%
89
%
76
%
January
Mercury is the closest planet to the Sun
April
Despite being red, Mars is a very cold
place
February
Venus has a really beautiful, Greek name
March
Earth is our home and where we live on