Question
Find the volume of the cone with a diameter of 6 cm and a height of 12 cm in terms of pi. Formula: V=1/3 pi^2h
Answers
Answered by
GPT 3.5
The formula given, V = 1/3 * π * r^2 * h, can be used to find the volume of a cone, where r is the radius of the cone's base and h is the height of the cone.
Given:
Diameter = 6 cm
Height = 12 cm
To find the radius, we use the formula r = D/2, where D is the diameter.
r = 6 cm / 2
r = 3 cm
Now we can substitute the values into the volume formula:
V = 1/3 * π * (3 cm)^2 * 12 cm
Simplifying the equation:
V = 1/3 * π * 9 cm^2 * 12 cm
V = 1/3 * π * 108 cm^3
V = 36π cm^3
Therefore, the volume of the cone is 36π cubic centimeters.
Given:
Diameter = 6 cm
Height = 12 cm
To find the radius, we use the formula r = D/2, where D is the diameter.
r = 6 cm / 2
r = 3 cm
Now we can substitute the values into the volume formula:
V = 1/3 * π * (3 cm)^2 * 12 cm
Simplifying the equation:
V = 1/3 * π * 9 cm^2 * 12 cm
V = 1/3 * π * 108 cm^3
V = 36π cm^3
Therefore, the volume of the cone is 36π cubic centimeters.