Answer:
radius = 4 inches
height = 24 inches
Step-by-step explanation:
The formula of the volume of a cone is:
V = (1/3) * pi * r^2 * h
where V is the volume, r is the radius of the base and h is the height.
We know that the height is 6 times greater than the base radius, so:
h = 6*r
If the volume is 401.92 in3, we can calculate the radius and the height of the cone:
401.92 = (1/3) * 3.14 * r^2 * 6*r
(1/3) * 3.14 * 6 * r^3 = 401.92
r^3 = 401.92 / ((1/3) * 3.14 * 6) = 64
r = 4 inches
h = 6*r = 6*4 = 24 inches.
Answer: The cone’s radius is 4 inches and it’s height is 24 inches
Step-by-step explanation: If the height is six times the radius, and the radius is r, then the height shall be 6 times r which equals 6r.
The volume is also given as 401.92. If the volume of a cone is given as
Volume = Pi x r^2 x (h/3)
401.92 = 3.14 x r^2 x (6r/3)
401.92 = 3.14 x r^2 x 2r
By cross multiplication we now have
401.92/3.14 = 2r^3
128 = 2r^3
128/2 = r^3
64 = r^3
Add the cube root sign to both sides of the equation
4 = r
Since the height is given as six times greater than the radius,
Height = 6r
Height = 6 x 4
Height = 24
Therefore the dimensions are,
Radius = 4 inches
Height = 24 inches
