A right circular cone has a base diameter of 10 and a height of 18. A second right circular cone has a base diameter of 15. If the volume of the second cone is equal to the volume of the first cone, then what is the height of the second cone?
(1/3) pi r^2 h = (1/3) pi R^3 H
so
r^2 h = R^2 H
(1/4)15^2 * h = (1/4)10^2 * 18
h = (100/225) * 18
God bless you Damon and I hope you have a lovely day!
To solve this problem, we can start by finding the volume of the first cone and then equating it to the volume of the second cone.
The volume of a right circular cone can be calculated using the formula:
V = (1/3) * π * r^2 * h
where V is the volume, π is a mathematical constant (approximately 3.14), r is the radius of the cone's base, and h is the height of the cone.
Given that the base diameter of the first cone is 10, we can find the radius (r) by dividing the diameter by 2:
r = 10 / 2 = 5
Now, substituting the values into the formula for the first cone:
V1 = (1/3) * π * 5^2 * 18
= (1/3) * 3.14 * 25 * 18
= 4710 cubic units (rounded to the nearest whole number)
Since the volumes of the first and second cones are equal, we have:
V1 = V2
4710 = (1/3) * π * (7.5)^2 * h2
To find the height of the second cone (h2), we can rearrange the equation:
h2 = (4710 * 3) / (π * 7.5^2)
Calculating this expression gives us:
h2 = 57.96 units (rounded to the nearest hundredth)
Therefore, the height of the second cone is approximately 57.96 units.