Acorns height is six times greater than the measurement of the cones radius the volume of a cone is 401.92 inches^3 what are the cones dimensions? Use 3.14 for pi

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

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.