A cone, a cylinder, and a sphere all have the same radius with the height of the cone and the cylinder being 2 times the radius. Match the statements that go together.
Column A
1.
The volume of 3 Cones:
The volume of 3 Cones
2.
The volume of 2 Cones:
The volume of 2 Cones
3.
The volume of 1 Sphere:
The volume of 1 Sphere
4.
The volume of 1 Cone:
The volume of 1 Cone
Column B
a.2/3 the volume of one Cylinder
b.The volume of one Cylinder
c.The volume of one Sphere
d.1/3 the volume of one Cylinder
1. The volume of 3 Cones: d.1/3 the volume of one Cylinder
2. The volume of 2 Cones: a.2/3 the volume of one Cylinder
3. The volume of 1 Sphere: c.The volume of one Sphere
4. The volume of 1 Cone: b.The volume of one Cylinder
1. The volume of 3 Cones: d.1/3 the volume of one Cylinder
2. The volume of 2 Cones: a.2/3 the volume of one Cylinder
3. The volume of 1 Sphere: c.The volume of one Sphere
4. The volume of 1 Cone: b.The volume of one Cylinder
Column A:
1. The volume of 3 Cones
2. The volume of 2 Cones
3. The volume of 1 Sphere
4. The volume of 1 Cone
Column B:
a. 2/3 the volume of one Cylinder
b. The volume of one Cylinder
c. The volume of one Sphere
d. 1/3 the volume of one Cylinder
Matching the statements from Column A to Column B:
1. The volume of 3 Cones - a. 2/3 the volume of one Cylinder
2. The volume of 2 Cones - d. 1/3 the volume of one Cylinder
3. The volume of 1 Sphere - c. The volume of one Sphere
4. The volume of 1 Cone - b. The volume of one Cylinder
To solve this problem, we first need to know the formulas for finding the volume of a cone, cylinder, and sphere.
The volume of a cone is given by the formula:
Vcone = (1/3) * π * r^2 * h
The volume of a cylinder is given by the formula:
Vcylinder = π * r^2 * h
The volume of a sphere is given by the formula:
Vsphere = (4/3) * π * r^3
Given that the height of both the cone and the cylinder is 2 times the radius, we can substitute 2r for h in the formulas.
Now let's match the statements in Column A with the correct descriptions in Column B:
1. The volume of 3 Cones
This means we need to find the volume of 3 cones, so we can use the formula Vcone = (1/3) * π * r^2 * h. Since all three cones have the same radius and height, their volumes will be the same.
Match: b. The volume of one Cylinder (since the volume of three cones is equal to the volume of one cylinder)
2. The volume of 2 Cones
This means we need to find the volume of 2 cones using the formula Vcone = (1/3) * π * r^2 * h. Again, since both cones have the same radius and height, their volumes will be the same.
Match: d. 1/3 the volume of one Cylinder (since the volume of two cones is equal to 1/3 of the volume of one cylinder)
3. The volume of 1 Sphere
This means we need to find the volume of 1 sphere using the formula Vsphere = (4/3) * π * r^3. Since there is only one sphere, its volume will not be compared to other shapes.
Match: c. The volume of one Sphere
4. The volume of 1 Cone
This means we need to find the volume of 1 cone using the formula Vcone = (1/3) * π * r^2 * h. The volume of one cone will be compared to another shape.
Match: a. 2/3 the volume of one Cylinder (since the volume of one cone is 2/3 of the volume of one cylinder)