If the height of the cone is 5 cm and the volume is 500 cm^3, what is the radius of the cone?
a
The radius is the same as a cylinder with a volume 500(3) and same height.
b
The radius is the same as a cylinder with a volume of 500/3 and the same height.
c
The radius is the same as a cylinder with the same volume and height of 5/3.
d
The radius is the same as a cylinder with the same volume and same height.
what are all of the answers
d
The radius is the same as a cylinder with the same volume and same height.
V of cone = (1/3) π (r^2) h
500 = (1/3)π(r^2)(5)
300/π = r^2
r = √(300/π) = appr 9.77 cm
To find the radius of the cone, you can use the formula for the volume of a cone, which is given by:
V = (1/3) * π * r^2 * h,
where V is the volume, r is the radius, and h is the height of the cone.
In this case, the height of the cone is given as 5 cm, and the volume is given as 500 cm^3.
Substituting these values into the formula, we have:
500 = (1/3) * π * r^2 * 5.
To find the radius, we need to rearrange the equation to solve for r.
Dividing both sides of the equation by (1/3) * π * 5 gives:
500 / ((1/3) * π * 5) = r^2.
Simplifying the right side, we have:
500 / ((1/3) * π * 5) = r^2,
100 / (π) = r^2.
To solve for r, take the square root of both sides of the equation:
√(100 / π) = r.
So the radius of the cone is √(100 / π).
By calculating this value, you will find that the radius is approximately 5.64 cm.
Therefore, none of the given options a, b, c, or d are correct.