a cone has a height of 6.if the volume of the cone is 24xpi, what is the radius of the cone?
volumecone=1/3 * PI*radius^2*h
solve for radius.
radius^2=3*24 /6=12
radius=2sqrt3
To find the radius of the cone, we can use the formula for the volume of a cone:
V = (1/3)πr^2h
where V is the volume, π is Pi, r is the radius, and h is the height.
In your case, the volume is given as 24π, and the height is given as 6. So, we can rewrite the formula as:
24π = (1/3)πr^2(6)
Simplifying further, we have:
24 = (1/3) * r^2 * 6
By canceling out the common factors, we get:
8 = r^2 * 2
Now, divide both sides of the equation by 2:
4 = r^2
To find the value of the radius, we take the square root of both sides of the equation:
sqrt(4) = sqrt(r^2)
Simplifying further:
2 = r
Therefore, the radius of the cone is 2 units.