A cylinder has a volume of 200in^3 Determine the volume of a cone whose radius and height are equal to that of the cylinder.
Volume of a cylinder = pi*(r^2)*h
r=h
http://math.about.com/od/formulas/ss/surfaceareavol_3.htm
Substitute r for h and solve for h, which is also equal to r. Then, substitute the values into the equation of volume of a cone.
volume of a cone= 1/3 pi*(r^2)*h
http://math.about.com/od/formulas/ss/surfaceareavol_2.htm
200
To determine the volume of the cone, we can use the formula:
Volume of a Cone = (1/3) * π * r^2 * h,
where r is the radius and h is the height of the cone.
Given that the radius and height of the cone are equal to that of the cylinder, we can assume that r represents the radius and h represents the height of the cylinder as well.
We know that the volume of the cylinder is 200 in^3. The formula for the volume of a cylinder is:
Volume of a Cylinder = π * r^2 * h
Since the radius and height of the cylinder are equal to the radius and height of the cone, we can rewrite the formula as:
200 = π * r^2 * r
Simplifying this equation, we have:
200 = π * r^3
To determine the value of r, let's rearrange the equation:
r^3 = 200 / π
Now, take the cube root of both sides:
r = (200 / π)^(1/3)
Now that we have the value of r, we can determine the volume of the cone using the formula for the volume of a cone:
Volume of the Cone = (1/3) * π * r^2 * r
Substituting the value of r we just found:
Volume of the Cone = (1/3) * π * ((200 / π)^(1/3))^2 * (200 / π)^(1/3)
Simplifying this expression will give us the final answer.