A cylinder made out of sheet metal is 4 feet long and 2 feet in diameter. What is the total surface area of sheet metal (including the circular ends of the cylinder).
1. First, break up the cylinder into like-geometries. In this case, the circular ends and the main cylinder: 2 x circle surface area + 1 x cylinder surface area = total surface area 2. Then, translate into the mathematical definition of the area of a circle, and surface area of a cylinder: 2 x (pi x r x r) + (2 x pi x r x h) = total surface area 3. Input the values given into the equation: pi = 3.14 r = 1 foot h = 4 feet 2 x (3.14 x 1 x 1) + (2 x 3.14 x 1 x 4) = total surface area 4. Using order of operations, solve: 2 x 3.14 + 25.12 = total surface area 6.28 + 25.12 = total surface area 31.4 = total surface area
If you have 150 followers on Twitter, and a new post of your cat increases your number of followers by 20%, how many followers do you have now?
1. To determine how many more followers you have, think of the problem as if you're adding new followers to the number of followers you already have: 150 + 20% = new number of followers 2. To be able to add these numbers, we need to change the percentage into a whole number: 20% can be written as 20/100, and when multiplied by the original 150, we get 20% of 150: 150 + 150 x 20/100 = new number of followers 2a. Sometimes, when multiplying large numbers, I find it easier to reduce the fraction to a smaller number by dividing by the greatest common factor first: 20/100 has a greatest common factor of 20, so when the numerator and denominator are both divided by 20, we get 1/5. 3. Now, we can return to multiplying. First change both numbers into fraction form, then multiply the numerator by the numerator and the denominator by the denominator: 150 + 150/1 x 1/5 = new number of followers 150 + 150/5 = new number of followers 2c. Then, reduce the fraction by dividing the numerator by the denominator: 150 + 30 = new number of followers 3. Finally, we can add the original 150 followers to the 30 followers you gained to get your total new number of followers: 150 + 30 = 180 followers Tip: Remember your order of operations!
10x + 8 = 4 - 6x Find x.
1. To find x, first bring like-terms to each side (note that every time you move a term to the other side of the equal sign, the sign changes): 10x + 6x = 4 - 8 2. Add or subtract like-terms: 16x = -4 3. Divide to isolate x: x = -4/16 4. Simplify the fraction by dividing by the greatest common factor: x = -1/4