Please Help me!!
1.
The volume of the cylinder = _____?:
2.
Is the volume of the sphere 2 times the volume of the volume of this cone?
3.
In order for the volume of the cone + the volume of the sphere = the volume of the cylinder, the height would have to be ____, not 3r?:
4.
The volume of a cylinder is ______ larger than the volume of a cone:
1. The volume of the cylinder = πr2h, where r is the radius and h is the height.
2. No, the volume of the sphere is not 2 times the volume of the cone.
3. In order for the volume of the cone + the volume of the sphere = the volume of the cylinder, the height would have to be 2r, not 3r.
4. The volume of a cylinder is πr2h larger than the volume of a cone.
Here are the answer choices I forgot to add it
You have to match them with the right answer. Thank you for your help
Column B
a.1/3 r
b.
75π
c.4r
d.2r
e.never
f.always
g.125π
h.sometimes
i.no
1. The volume of a cylinder is calculated using the formula V = πr^2h, where r is the radius of the base and h is the height. Fill in the appropriate values for r and h to find the volume.
2. To compare the volume of a sphere and a cone, we need more information. The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere. The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. You can compare the two volumes by substituting the values of r and h for each shape and determining if they are equal or not.
3. The volume of a cone plus the volume of a sphere will not be equal to the volume of a cylinder if the height of the cone is not equal to 3 times the radius of the base (3r). The exact value of the height needed for the volumes to be equal will depend on the specific dimensions of the shapes involved.
4. The volume of a cylinder is typically greater than the volume of a cone because the cylinder has a larger base and/or greater height. However, the actual size difference will depend on the specific dimensions of the cone and cylinder being compared.
1. To find the volume of a cylinder, you can use the formula V = πr²h, where V represents the volume, π represents pi (approximately 3.14159), r represents the radius of the base, and h represents the height. You need to know the values of the radius and height to calculate the volume.
2. To compare the volume of a sphere and a cone, you need to know their respective formulas. The formula for the volume of a sphere is V = (4/3)πr³, where r represents the radius. The formula for the volume of a cone is V = (1/3)πr²h, where r represents the radius and h represents the height. If the volume of the sphere is twice the volume of the cone, you can set up the equation (4/3)πr³ = 2 * (1/3)πr²h and solve for the variables.
3. To find the necessary height for the volume of the cone plus the volume of the sphere to equal the volume of the cylinder, you can set up the equation Vcone + Vsphere = Vcylinder. Plug in the appropriate formulas for each shape, considering the known variable values. Solve for the height variable to find the value that satisfies this equation.
4. To determine the volume difference between a cylinder and a cone, you need to calculate the volumes of both shapes. Subtract the volume of the cone from the volume of the cylinder to find the difference. Use the formulas Vcone = (1/3)πr²h and Vcylinder = πr²h to calculate their respective volumes, and then subtract one from the other to get the answer.