1. How many Cones in a Sphere with the same radius and height = 2r?
2. How many Cones in a Cylinder with the same radius and height?
3.How many spheres in a cylinder with the same radius and h = 2r?
5 Problems - SHOW ALL WORK!
1. What is the similarity and difference in finding the volume of cone, cylinder, and sphere?
2. Three friends are sharing a soda from a can. The dimensions of a soda can are shown below. If the three friends each drank an equal portion how much soda would each friend drink in terms of pi?
3. Doug has a bucket that is 12in tall and has a radius of 6in filled completely with water. Dough pushes a basketball with a diameter of 10in completely into the water overflowing the water in the bucket. How much water is left in the bucket?
4. Crystal was told by her mom she could get one scoop of candy. There are two scoops and both scoops are shaped like cones. Given the dimensions below which cone should Crystal use if she wants to get the greatest amount of candy?
Cone A: 30 cm width,15 cm height,15 cm radius
Cone B: 15 cm width,30 cm height, 7.5 cm radius
5. In your opinion, what is the most important thing to remember to do when solving problems involving volume?
Answer each question
1.
- The number of Cones in a Sphere with the same radius and height = 2r would be 6.
Explanation: If we imagine a sphere inscribed within a cube, the cube can be divided into 6 identical cones with the top of each cone touching the center of the sphere.
2.
- The number of Cones in a Cylinder with the same radius and height would be 3.
Explanation: If we imagine a cylinder inscribed within a cube, the cube can be divided into 3 identical cones with the top of each cone touching the center of the cylinder.
3.
- The number of spheres in a cylinder with the same radius and h = 2r would be 2.
Explanation: The cylinder can be inscribed within a cube, and the cube can be divided into 2 identical spheres with each sphere touching the top and bottom of the cylinder.
1.
- The similarity in finding the volume of cone, cylinder, and sphere is that they all involve using the formula V = 1/3πr^2h for a cone, V = πr^2h for a cylinder, and V = 4/3 πr^3 for a sphere. The difference lies in the dimensions used (radius and height) in each formula.
2.
- Each friend would drink 1/3 of the soda can. So, each friend would drink π/3 cubic units of soda.
3.
- The amount of water left in the bucket would be the volume of the cylinder formed by the original water + the volume of the basketball that was pushed in and overflowing. The volume of the remaining water can be calculated using the formula for the volume of a cylinder.
4.
- Crystal should choose Cone A to get the greatest amount of candy as it is larger in volume compared to Cone B. The volume of each cone can be calculated using the formula V = 1/3πr^2h.
5.
- The most important thing to remember when solving problems involving volume is to correctly identify the shape (cone, cylinder, sphere), use the appropriate formula for that shape, and pay attention to the dimensions given in the problem to accurately calculate the volume.