Volume of a Cone Solving for Radius and Height

hey guys today we are going to be working with the volume of cone but we're going to be using the volume of cone to soloft for radius and also use volume to solof for height so our steps in this process are to First write down your formula and then substitute the given information into the formula and then use inverse operations to isolate or solve for the missing measurement so the volume of tone formula is Pi square time height which if you remember that's the same as the cylinder formula but we're going to take that value and divide by three because it takes three cones to fill cylinder and then another way we could write that formula is 1/3 * < r^ 2 * height where is the radius is the height let's keep in mind what the radius measurement is the radius is the center of the circle to the outside of the circle and height is the distance from the point of the cone down to the center of the circle also another important measurement you need to remember is diameter and that's the distance all the way across the circle through the center of the circle and so if you're given diameter you have to divide that number in half to get radius all right so let's do an example where we are solving for height first thing we want to do is write our formula down volume equals < r^ 2 * height / 3 don't forget that dividing by three part it's easy to forget we're going to substitute 47.1 in for the volume and then 3.14 for pi and the radius is three so we're going to square that so that means I'm going to use it as factor twice so I'm going to write it two times and then height divided by three all right so the next thing we're going to do is go ahead and multiply Pi * 3 * 3 divided 3 so 47.1 is equal to when calculate that value get 9.42 times we're going to bring down into the next step of our work and divide now we're going to divide by 9.42 the inverse oper ation of multiplying 9.42 * would be to divide by 9.42 so we're going to do that on both sides of the equal sign and our height is going to equal 5 and that measurement is not cubed because it's just the height measurement and that is one dimension let's go to the next example where we solve for radius okay so we're going to write our formula again we're solving for con of the radius of cone so volume equal piun r^ 2 * height / 3 we're going to substitute 3768 in for volume so that's 3768 = Pi which is 3.14 times the radius squared which we don't know so we're going to put that down as 2 and then the height is 10 so we're going to substitute it's okay if write the 10 before the squ the order doesn't matter when we are multiplying and then finally divide by three so the first thing would like for you to do is plug in 3.14 * 10 and divide that value by three that does give you repeating decimal it's 10.4 6666666 we're going to round that to 467 okay the more you can carry out these three digits or this number the more accurate your answer is going to be that repeating decimal kind of makes things little different all right 3768 comes down to the next step of the problem so the next thing we'll do is divide by 10467 just like we did when we saw for high okay we get R2 equals and you get 35.99 something go ahead and round that to 36 right so that's going to give you perfect square and finally we are going to take the square root of both sides to solve for radius so is going to equal 6 and again that's not millimet cubed because we are just solving four radius hope this video was helpful good luck on your quiz