The relationships of the volumes of cylinders, cones, and spheres (considering that the height and radius are the same for all of the objects):
Put the items in order from least amount needed to greatest amount needed.
Reorder answers
1.Number of Cones needed to equal the volume of one Cylinder
Reorder answers
2.Number of Cones needed to equal the volume of one Sphere
Reorder answers
3.Number of Cones needed, along with 1 Sphere to equal the volume of one Cylinder
Reorder answers
4.Number of Spheres needed to equal the volume of one Cylinder
Reorder answers
5.Number of Spheres needed to equal the volume of one Cone
Answer:
1.Number of Spheres needed to equal the volume of one Cone
2.Number of Cones needed to equal the volume of one Sphere
3.Number of Spheres needed to equal the volume of one Cylinder
4.Number of Cones needed, along with 1 Sphere to equal the volume of one Cylinder
5.Number of Cones needed to equal the volume of one Cylinder
To compare the volumes of cylinders, cones, and spheres, we can use the following formulas:
Cylinder volume: Vc = πr^2h
Cone volume: Vcn = (1/3)πr^2h
Sphere volume: Vs = (4/3)πr^3
Considering that the height and radius are the same for all objects, we can compare their volumes based on the ratios between their formulas.
1. Number of Cones needed to equal the volume of one Cylinder:
The volume of a cone is one-third the volume of a cylinder with the same radius and height. Therefore, we need 3 cones to equal the volume of one cylinder. Reorder: 3
2. Number of Cones needed to equal the volume of one Sphere:
The volume of a cone is (3/4) times the volume of a sphere with the same radius. Therefore, we need (4/3) cones to equal the volume of one sphere. Reorder: (4/3)
3. Number of Cones needed, along with 1 Sphere, to equal the volume of one Cylinder:
From the first comparison, we know that 3 cones are needed to equal the volume of one cylinder. Additionally, it would take 1 sphere to match the volume of the cylinder. So, in total, we would need 3 cones and 1 sphere to equal the volume of one cylinder. Reorder: 3 + 1
Therefore, the correct order from least amount needed to greatest amount needed is:
1. Number of Cones needed to equal the volume of one Cylinder: 3
2. Number of Cones needed to equal the volume of one Sphere: (4/3)
3. Number of Cones needed, along with 1 Sphere, to equal the volume of one Cylinder: 3 + 1