Question

Three water storage containers have the same volume in the shape of a cylinder, a cone, and a sphere. The base radius of the cylinder, the base radius of the cone, and the radius of the sphere are equal.

The ratio of the height of the cone to the height of the cylinder is
Select one
3 to 1
2 to 1
1 to 1
3 to 1
2 to 1
1 to 1

The ratio of the height of the cone to radius of the sphere is
the base radius of the cone, and the radius of the sphere are equal.

the base radius of the cone, and the radius of the sphere are equal.

1 to 1
4 to 1
9 to 1
1 to 1
4 to 1
9 to 1

Answer 1

Answer:

The ratio of the height of the cone to the height of the cylinder is 3 to 1

The ratio of the height of the cone to the radius of the sphere is 4 to 1

Step-by-step explanation:

First we need to know the volume of a cylinder, a cone and a sphere:

V_cylinder = pi*r^2*h

V_cone = (1/3)*pi*r^2*h

V_sphere = (4/3)*pi*r^3

If they have the same volume:

The ratio of the height of the cone to the height of the cylinder is:

V_cone / V_cylinder = 1

(1/3)*pi*r^2*h1 / pi*r^2*h2 = 1

(1/3) * h1 = h2

h1 / h2 = 3

So the ratio is 3 to 1

The ratio of the height of the cone to the radius of the sphere is:

V_cone / V_sphere = 1

(1/3)*pi*r^2*h / (4/3)*pi*r^3 = 1

h / 4r = 1

h / r = 4

So the ratio is 4 to 1