The volume of a right circular cone is 150 pie cubic centimetrs. Find its altitude in centimeters if the radius of the base is 5cm.
v = pi r^2 h
so h = v / (pi r^2)
= 150 pi /25 pi
= 6
To find the altitude of a right circular cone, you can use the formula for the volume of a cone, which is given by:
V = (1/3) * π * r^2 * h,
where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the altitude.
Given that the volume of the cone is 150π cubic centimeters and the radius of the base is 5 cm, we can substitute these values into the formula:
150π = (1/3) * π * 5^2 * h.
To simplify the equation, we can cancel out the π on both sides:
150 = (1/3) * 5^2 * h.
Now, simplify the equation further:
150 = (1/3) * 25 * h.
Multiply both sides by 3:
450 = 25h.
Divide both sides by 25:
h = 18.
Therefore, the altitude of the cone is 18 centimeters.