a cone has a circular base of radius 16cm and a volume of 420cm2.find the height of the cone.
1.56
1.56 cm
To find the height of the cone, we can use the formula for the volume of a cone:
Volume = (1/3) * π * r^2 * h
where r is the radius of the base and h is the height of the cone.
In this case, we are given that the radius of the base is 16 cm and the volume is 420 cm^3.
Substituting these values into the formula, we have:
420 = (1/3) * π * (16^2) * h
Now, let's solve for h:
420 = (1/3) * π * 256 * h
Dividing both sides of the equation by ((1/3) * π * 256), we get:
h = 420 / ((1/3) * π * 256)
Simplifying further, we have:
h = 420 / (256/3)π
h = (420 * 3) / (256π)
h ≈ 4.90 cm
Therefore, the height of the cone is approximately 4.90 cm.