A cone has a radius of 4 feet on its base. The approximate volume of the
cone is 189 ft^3. Determine the height of the cone to the nearest tenth of a
foot. Use 3.14 for π. (5 points)
Use the reciprocal to get about ______.
a. 504 = pi h
b. 35.4 = pi h
c. 1008 = pi h
d. 23.6 = pi h
Let's start by using the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
Since the volume of the cone is given as 189 ft^3 and the radius is 4 feet, we can plug in these values:
189 = (1/3) * 3.14 * 4^2 * h
189 = (1/3) * 3.14 * 16 * h
189 = 16.75 * h
h = 189 / 16.75
h ≈ 11.25 feet
So, the height of the cone is approximately 11.25 feet. Using the reciprocal of this value, we get:
1 / 11.25 ≈ 0.0888888888...
Rounded to the nearest tenth, the reciprocal of the height of the cone is 0.1.
Therefore, the answer is approximately:
b. 35.4 = π h