# Algebra begginer

#### alex88

##### New member
Hello friends
I've joined this forum in hopes that i can improve my mathematics skills. I've always lacked them and had no need for advanced (advanced to me lol) maths, untill now.
I have an exam for a serious job im applying for and ive purchased the practice exams to study. I've reached a point where i have absolutely no idea where to start my calculations.
Ill attach the image of the question.
Please don't tell me the answers, only the basic formula i need to use to calculate the 2 questions. Im sure this is baby maths for some people, but for me its not.
Alex

#### Subhotosh Khan

##### Super Moderator
Staff member
Hello friends
I've joined this forum in hopes that i can improve my mathematics skills. I've always lacked them and had no need for advanced (advanced to me lol) maths, untill now.
I have an exam for a serious job im applying for and ive purchased the practice exams to study. I've reached a point where i have absolutely no idea where to start my calculations.
Ill attach the image of the question.
Please don't tell me the answers, only the basic formula i need to use to calculate the 2 questions. Im sure this is baby maths for some people, but for me its not.
Alex

Hints:

What is the surface area of each of the bases (two) of a cylinder?

What is the surface area of a cylinder - excluding the two bases?

If you do not know start by googling those terms.

#### JeffM

##### Elite Member
Hello friends
I've joined this forum in hopes that i can improve my mathematics skills. I've always lacked them and had no need for advanced (advanced to me lol) maths, untill now.
I have an exam for a serious job im applying for and ive purchased the practice exams to study. I've reached a point where i have absolutely no idea where to start my calculations.
Ill attach the image of the question.
Please don't tell me the answers, only the basic formula i need to use to calculate the 2 questions. Im sure this is baby maths for some people, but for me its not.
Alex

This is an exercise in using formulas. To my mind, this is the most frequent practical use of algebra for the majority of people.

A fundamental idea in algebraic notation is to use letters for numbers that we do not yet know. When you see a letter in algebra, such as x, it usually means "some number, but because we don't know yet what number we are talking about, we are going to call it x." It's like calling a thing that you don't know the name of a "thingumajig." Got that?

Formula tell us arithmetical relationships that are always true between different quantities. You do not have to remember that a rectangle with width 6 and height 8 has an area of 48 whereas a rectangle with width 7 and height 3 has an area of 21. You remember (or look up) the general formula that the area of a rectangle is the width times the height, or, in algebraic notation a = hw.

In algebraic notation, we almost never use $$\displaystyle \times$$ to mean times. It is to easy to confuse with the letter X. Instead, we write things like 3z or 3 * z, both of which means 3 times whatever number z happens to be. To save time, we also write

$$\displaystyle r^2 = r * r, \ r^3 = r * r * r, \text { and } r^4 = r * r * r * r.$$

There is a lot more to learn about algebraic notation, but that will get you started.

Because we use letters to represent numbers and the letters can represent different numbers in different problems, it is good practice to write down what each letter stands for in each problem.

So the meanings in use in problems 25 and 26 are

$$\displaystyle r = \text {radius of cylinder;}$$

$$\displaystyle h = \text {height of cylinder;}$$

$$\displaystyle b= \text {surface area of the base of a cylinder;}$$

$$\displaystyle s = \text {surface area of the sides of a cylinder;}$$

$$\displaystyle v = \text {volume of a cylinder; and}$$

$$\displaystyle \pi \approx 3.14.$$ This is an approximation, not a strict equality.

Now you know what the letters stand for in these two problems. The book was lazy because they gave only some of them, but you can assign your own. Then the book gives you some of the formulas you need. Here are the ones you actually need.

$$\displaystyle b = \pi r^2.$$

$$\displaystyle s = 2 \pi rh.$$

$$\displaystyle v = \pi r^2h.$$

The point is that these work for all cylinders. So you can use them for any cylinder if you know r and h.

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#### alex88

##### New member
Hello
Thank you both for the reply. I understand some of what you are saying, however, my maths is so limited that when i look at question 25 for example, i dont know what formula to use. Should i just "know" what formula to use? How do i learn what formulas answer what question?
In regards to question 25, i know i need a formula to find the surface area, but what formula is needed, i have no idea. I know how to designate letters to an unknown value but thats as far as i go lol.
Sorry for my lack of understanding. Im doing many maths tests online every day for the past 2 weeks. Nothing along the lines of algebra though, more abstract and reasoning.
Thanks again.

#### Otis

##### Senior Member
… Should i just "know" what formula to use? …
Yes. If your goal is to determine measurements like the circumference of a circle, or the area of a circle, or the area of a rectangle, or the volume of a cylinder, then you ought to memorize each of those formulas.

I assume that you know what their above-ground swimming pool looks like. Its volume is a cylinder.

Consider just the wall of the pool (that is, just the side of the cylinder -- not its base). The diagram shows a section of this wall, where they've labeled its height. If you were to cut the wall along one of those vertical lines they've drawn, and then unroll the steel so that it was lying flat on the ground, what shape would it be?

If you know the shape, then calculate its area. If you're not sure, roll a piece of typing paper into a cylinder shape, and think about it.

Now consider the circular base. Calculate its area, also. (They gave you the formula.)

Add these two areas together, and round the result UP to a Whole number.

For the second question, they gave you the formula for the volume of a cylinder. Substitute in the known values for radius and height, and do the arithmetic. Round the result to the NEAREST Whole number.

I note that you've been given somewhat sloppy notation. They wrote the formula for circular area as $$\displaystyle \pi r2$$, but it's supposed to be $$\displaystyle \pi r^2$$. They wrote the formula for the cylinder volume as $$\displaystyle \pi r2 h$$, but it's supposed to be $$\displaystyle \pi r^2 h$$.