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:
d
The volume of 3 Cones
2.
The volume of 2 Cones:
a
The volume of 2 Cones
3.
The volume of 1 Sphere:
c
The volume of 1 Sphere
4.
The volume of 1 Cone:
b
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
To match the statements in Column A with the appropriate statements in Column B, we need to use the formulas for the volumes of cones, cylinders, and spheres.
The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius and h is the height.
The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.
Given that the height of the cone and the cylinder is 2 times the radius, we can use this information to determine the corresponding statements in Column B.
1. The volume of 3 Cones:
To find the volume of 3 cones, we need to multiply the volume of 1 cone by 3. Since the height of the cone is 2 times the radius, the volume of 1 cone is V = (1/3)πr²(2r) = (2/3)πr³. Therefore, the volume of 3 cones is (2/3)πr³ * 3 = 2πr³. This matches with statement b. 2/3 the volume of one Cylinder.
2. The volume of 2 Cones:
Similar to the previous calculation, we need to find the volume of 1 cone and then multiply it by 2. The volume of 2 cones is (2/3)πr³ * 2 = (4/3)πr³. This matches with statement a. The volume of one Cylinder.
3. The volume of 1 Sphere:
The volume of 1 sphere is given by V = (4/3)πr³. This matches with statement c. The volume of one Sphere.
4. The volume of 1 Cone:
The volume of 1 cone is (1/3)πr²(2r) = (2/3)πr³. This matches with statement d. 1/3 the volume of one Cylinder.
In conclusion:
1. The volume of 3 Cones: b. 2/3 the volume of one Cylinder
2. The volume of 2 Cones: a. The volume of one Cylinder
3. The volume of 1 Sphere: c. The volume of one Sphere
4. The volume of 1 Cone: d. 1/3 the volume of one Cylinder