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.

Thank you for reading and your assistance in advance.

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.