A cone just fits inside a cylinder with volume 300cm^3. What is the volume of the cone?
1/3 as much.
Check out the formulas for the volumes of a cylinder and cone. One is one-third of the other, for the same r and h.
thanks.
But I don't understand what you said.can you explain to me properly.
To find the volume of the cone, we need to know the height and radius of the cone. One way to determine those values is to consider the fact that the cone can completely fit inside the cylinder with volume 300 cm^3.
The volume of a cylinder is given by the formula:
V_cylinder = π * r^2 * h
Where r is the radius of the cylinder and h is its height.
Since the cone fits completely into the cylinder, its volume must be equal to or less than the volume of the cylinder. Therefore, V_cone ≤ V_cylinder = 300 cm^3.
The volume of a cone is given by the formula:
V_cone = 1/3 * π * r^2 * h
We know that the volume of the cone is less than or equal to 300 cm^3, so we can write:
1/3 * π * r^2 * h ≤ 300 cm^3
Now we need to determine the radius and height of the cone. To do this, we can use the relationships between the dimensions of the cone and the cylinder.
The height of the cone must be equal to the height of the cylinder, as the cone fits completely inside it. So, h_cone = h_cylinder.
Next, we can determine the relationship between the radius of the cone and the radius of the cylinder. Since the cone just fits inside the cylinder, the radius of the cone must be smaller than the radius of the cylinder. Mathematically, we can express this as r_cone < r_cylinder.
Now, use these relationships to solve for the volume of the cone.