Question 20

Question 19 You can use a calculator on this one. What the students need to do is use the volume of the cone to find the volume of the sphere. Again, the formulas are not given to the students so they will need to know them. The volume of a Cone is V= (1/3)πr2h and the volume for sphere is V = (4/3)r3. Once the students find the volume of the cone, they plug that in to find the volume of the sphere. The next page will show that

Question 19 Cont V = πr2h diameter: 32 3 height: 27 32 2 = 16 32 2 = 16 V = (3.14)(16)2(27) 3 V = (3.14)(256)(27) 3 The formula for the volume of a Cone is V= (1/3)πr2h. In this initial problem, however, we are given the diameter and the height. We need the radius and the height. The first thing that we are going to is divide the diameter in half to get the radius. 32 divide by 2 is 16, so the radius is 16. After finding the radius, we can plug in the values that we know. We know that pi is 3.14, the radius is 16, and the height is 27. So we get that 3.14*162*27 all divided by 3. 16 squared is 256, so we do that to follow the order of operations. Following that, we multiply all of the numbers of top and we get 21,703.68. We then divide that by 3 and we get that the volume of the cone is 7,234.56. This value will continue to the next slide. V = 21703.68 3 V = 7234.56

√ √ Question 19 Cont V = 4 πr3 3 3( ) 7234.56 = 4(3.14) r3 3 ( ) 3 3( ) 7234.56 = 4(3.14) r3 3 ( ) 3 21703.68 = (4)(3.14)r3 This time, we know the volume and we are looking for the radius. In order to find the radius, we need to know that the formula for the volume of a sphere is (4/3)πr3. Once we know that, we can put in the values that we know, which are pi and the volume. In order to get rid of the fraction, the first thing you need to do is multiply both sides of the equation by 3. When you do that, the threes on the right hand side of the equation cancel out and you’re left with: 21703.68 = 4 * 3.14 * r3. Next, you multiply 4 and 3.14, and you get that: 21703.68 = 12.56r3 After this, you divide both sides by 12.56 in order to get r3 by itself. This leaves you with: 1728 = r3. Then, you take the cube root of both sides. When you do that, you get that the radius is 12. ________ 12.56 21703.68 = 12.56 r3 ________ 12.56 √ √ 1728 = r3 12 = r