Which ratio describes the relationship between the formulas for the volume of a cone to the volume of a sphere?(1 point)
its actually 1:2...
The ratio that describes the relationship between the formulas for the volume of a cone to the volume of a sphere is 1:3.
To determine the ratio between the volume of a cone and the volume of a sphere, we need to find the formulas for both.
The formula for the volume of a cone is given by:
V_cone = (1/3) * π * r^2 * h,
where π is a constant (approximately 3.14159), r is the radius of the base of the cone, and h is the height of the cone.
The formula for the volume of a sphere is given by:
V_sphere = (4/3) * π * r^3,
where π is the same constant, and r is the radius of the sphere.
Now, we can find the ratio between the two volumes by dividing the volume of the cone by the volume of the sphere:
Ratio = V_cone / V_sphere = [(1/3) * π * r^2 * h] / [(4/3) * π * r^3].
Next, simplify the expression by canceling out common terms:
Ratio = (1/3) * r^2 * h / (4/3) * r^3.
To simplify it further, we can cancel out the common factor of 1/3:
Ratio = r^2 * h / (4/3) * r^3,
Ratio = (3/4) * (r^2 * h) / r^3.
Therefore, the ratio between the volume of a cone to the volume of a sphere is:
(3/4) * (r^2 * h) / r^3.