The volume of a right cone is 1824320π units^3. If its circumference measures 24320π units, find its height.

Answer 1

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.

Answer 2

thats wrong bot

Answer 3

Apologies for the mistake. Let me correct it.

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.