The volume of a right cone is 1824320π units^3. If its circumference measures 24320π units, find its height.
Let the radius of the base of the cone be r and its height be h.
The formula for the volume of a cone is V = 1/3πr^2h. We are given that V = 1824320π, so we have:
1824320π = 1/3πr^2h
Simplifying, we have:
5464320 = r^2h
The formula for the circumference of a cone is C = 2πr. We are given that C = 24320π, so we have:
24320π = 2πr
Dividing both sides of the equation by 2π, we get:
12160 = r
Substituting this value of r into the equation 5464320 = r^2h, we have:
5464320 = (12160)^2h
Simplifying, we have:
5464320 = 147865600h
Dividing both sides of the equation by 147865600, we get:
h = 5464320/147865600
Simplifying, we have:
h = 0.037
Therefore, the height of the cone is approximately 0.037 units.
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The formula for the volume of a cone is V = 1/3πr²h, where r is the radius of the base and h is the height. We are given that the volume is 1824320π units³, so we have:
1824320π = 1/3πr²h
Simplifying, we have:
3 * 1824320 = r²h
5464320 = r²h
The formula for the circumference of a cone is C = 2πr. We are given that the circumference is 24320π units, so we have:
24320π = 2πr
Dividing both sides by 2π, we get:
12160 = r
Substituting this value of r in the equation 5464320 = r²h, we have:
5464320 = (12160²)h
Simplifying, we have:
5464320 = 147865600h
Dividing both sides by 147865600, we get:
h = 5464320 / 147865600
h ≈ 0.037
Therefore, the height of the cone is approximately 0.037 units.
To find the height of the right cone, we can use the formula for the volume of a cone and the formula for the circumference of a circle.
The formula for the volume of a cone is given as V = (1/3)πr^2h, where V is the volume, r is the radius of the base, and h is the height.
The formula for the circumference of a circle is given as C = 2πr, where C is the circumference and r is the radius. In this case, the circumference is given as 24320π units.
By rearranging the formula for circumference, we can solve for the radius as follows:
C = 2πr
24320π = 2πr
r = 24320π / 2π
r = 12160 units
Substituting the values for the volume and radius into the formula for the volume of a cone, we can solve for the height:
V = (1/3)πr^2h
1824320π = (1/3)π(12160^2)h
1824320π = 464486400πh
h = 1824320 / 464486400
h = 0.00393 units
Therefore, the height of the right cone is approximately 0.00393 units.