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:
b
The volume of 3 Cones
2.
The volume of 2 Cones:
c
The volume of 2 Cones
3.
The volume of 1 Sphere:
a
The volume of 1 Sphere
4.
The volume of 1 Cone:
d
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 correct statements in Column B, we need to understand the formulas for calculating the volumes of a cone, a cylinder, and a sphere.
The volume of a cone is given by the formula: V = (1/3) * π * r^2 * h, where V represents the volume, π represents pi (approximately 3.14159), r represents the radius, and h represents the height.
The volume of a cylinder is given by the formula: V = π * r^2 * h.
The volume of a sphere is given by the formula: V = (4/3) * π * r^3.
We are given that the height of the cone and cylinder is twice the radius. Let's call the radius "r". So, the height of the cone is 2r, and the height of the cylinder is also 2r.
Now, let's match the statements in Column A with the correct statements in Column B based on the formulas and the given information:
1. The volume of 3 Cones:
Since we have 3 cones with the same radius and height, their volumes will be the same. So, the correct match in Column B is d. 1/3 the volume of one Cylinder.
2. The volume of 2 Cones:
Again, they have the same radius and height. So, the correct match in Column B is a. 2/3 the volume of one Cylinder.
3. The volume of 1 Sphere:
The volume of a sphere is independent of the height. So, the correct match in Column B is c. The volume of one Sphere.
4. The volume of 1 Cone:
One cone has a radius and height. So, the correct match in Column B is b. The volume of one Cylinder.
Therefore, the correct matching of statements in Column A and Column B is:
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