Answer:
The ratio of the volume of cone to square pyramid is π or 3.14
Explanation:
Given
Shapes: Cone and Square Pyramid
Diameter of the cone, d = 10 inches
Height of the cone, h = 12 inches
Height of the pyramid, h = 12 inches
Base edge of the pyramid, a = 5 inches
Required:
Ratio of the volume of cone to square pyramid.
First, we calculate the volume of each shapes
Volume of a cone is calculated as follows;
Volume = ⅓πr²h
Where r = radius = ½d
Recall that d = 10 inches
So, r = ½ * 10 inches
r = 5 inches.
Hence,
Volume = ⅓ * π * 5² * 12
Volume = ⅓ * π * 25 * 12
Volunteer = π * 25 * 4
Volume = 100π in³
Calculating Volume of the pyramid.
Volume = ⅓a²h
Recall that a = 5 and h = 12
So, Volume = ⅓ * 5² * 12
Volume = ⅓ * 25 * 12
Volume = 25 * 4
Volume = 100 in³
Now that both volumes have been calculated.
The ratio of the volume of cone to square pyramid is calculated by dividing the volume of the cone by the volume of the square pyramid.
Ratio = 100π ÷ 100
Ratio = π
Taking π as 3.14
Ratio = 3.14
Hence, the ratio of the volume of cone to square pyramid is π or 3.14