Suppose an aluminium soup can in the shape of a right circular cylinder is 10 inches long and 4 inches in diameter. How much aluminium was used to make the can?
Two equations you need to know to solve this problem is the area of a circle and the surface area of a cylinder. Area of a circle: A = pi( r^2) where r= the radius of the circle Surface area of a cylinder: A = 2x pi x r x h where r = the radius of the cylinder and h = the height of the cylinder. Knowing these two equations we can figure out the total surface area of the can. Which is the surface area of the cylinder + 2 times the area of the circle ( because there are two circles, one at the bottom of the can and one at the top of the can) So now we plug in the information that we know. The diameter of both the circle and the cylinder is 4 in. The radius = diameter/2 therefore the radius of both is 2in. The height of the cylinder is 10 in. So the area of the circle = pi ( 2^2) which is equal to 12.56 in^2 The surface area of the cylinder = 2 x pi x 2in x 10in which is equal to 125.6 in^2 Therefore the total area of the can is = 125.6 in ^2 + 2(12.56in^2) = 150.72 in^2 So you would need 150.72 in^2 of aluminium to make this soup can.
Solve the following multiplication questions: 1) 1 x 2 = 2) 8 x 3 = 3) 4 x 4 =
1) For this multiplication problem there is a rule that is very helpful: 1 times any number is equal to that number. So whenever you have 1 times any number it is always going to be equal to that number. For example 1 x 7 = 7 and 1 x 4 = 4. Another way to think of it is you have one group of that number. So for this problem 1 x 2 = 2, because there is only one group of 2 or 2 groups of 1. It also helps to picture the numbers as real things. So you have 2 bags and each bag has 1 toy in it. How many toys do you have all together? Well you have 1 toy in the first bag + 1 toy in the second bag = 2 2) One way to do this problem is to think of it in groups. You have 8 groups of 3, or 3 groups of 8. So if you have 8 groups of 3, that would be 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 which is equal to 24. You can also have 3 groups of 8. So that would be 8 + 8 + 8 which is equal to 24. It does not matter which way you group the numbers. It also helps to picture the numbers as real things. So for example, you could have 3 bags and in each bag you have 8 apples. How many apples do you have in total? Well 8 in the first bag + 8 in the second bag + 8 in the third bag = 24 apples. 3) One way to do this problem is to think of it in groups. You have 4 groups of 4. So if you have 4 groups of 4 that would be 4 + 4 + 4 + 4 which is equal to 16. It also helps to picture the numbers as real things. So for example, you could have 4 bags and in each bag you have 4 pieces of candy. How many pieces of candy do you have? Well 4 in the first bag + 4 in the second bag + 4 in the third bag + 4 in the fourth bag = 16 pieces of candy.
Simplify: 13x^3 - 2x(12x^2 + 2x + 9) - 5x + 15
13x^3 - 2x(12x^2 + 2x + 9) - 5x + 15 1st step: Distribute the -2x to all three terms (12x^2+2x+9) = 13x^3 - 2x(12x^2) - 2x(2x) - 2x(9) - 5x + 15 =13x^3 - 24x^3 - 4x^2 - 18x - 5x + 15 2nd step: Combine like-terms 13x^3 - 24x^3 - 4x^2 - 18x - 5x + 15 (13x^3 - 24x^3) - 4x^2 (- 18x - 5x) + 15 = -11x^3 - 4x^2 - 23x +15 Final Answer: -11x^3 - 4x^2 - 23x +15