Cyclinder and cone base and height has same,volume cone is 30cm³,volume of cyclinder is??
What is the Radius and the Height? And is it a right Cylinder?
cone: v = 1/3 Bh
cylinder: v = Bh
so, with the same base and height, the cylinder has 3 times the volume of the cone.
To find the volume of a cylinder, we need to know the height and the area of the base. In this case, since the height of the cylinder and cone are the same, we only need to find the area of the cone's base to determine the volume of the cylinder.
Given that the volume of the cone is 30 cm³ and the height of both shapes is the same, we need to find the area of the cone's base. The formula for the volume of a cone is:
V = (1/3) * π * r² * h
In this case, we have V = 30 cm³. Let's assume the radius of the cone's base is r. Therefore, the formula becomes:
30 = (1/3) * π * r² * h
Since the height is the same for both the cone and cylinder, we can rewrite the formula as:
30 = (1/3) * π * r² * h ===> 30 = (1/3) * π * r² * h ===> 30 = (1/3) * π * r² * h
Now, let's solve for the area of the cone's base (π * r²):
(1/3) * (π * r²) * h = 30
π * r² = (30 * 3) / h
π * r² = 90 / h
Now, we can use the formula for the volume of a cylinder:
V = π * r² * h
Since the height of the cylinder and cone are the same, we can substitute the value of π * r² from above into the cylinder volume formula:
V_cylinder = (90 / h) * h
V_cylinder = 90
Therefore, the volume of the cylinder is 90 cm³.
To find the volume of a cylinder, you need to know the formula for calculating the volume of a cylinder, which is given by:
Volume of Cylinder = π * r^2 * h
Where:
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the base of the cylinder
- h is the height of the cylinder
From the given information, we know that the height of the cone is the same as the height of the cylinder. However, we don't have the specific values of the radius or height.
Therefore, without the specific values for radius and height, we cannot calculate the volume of the cylinder.