The volume of a cone is 8.1 cubic yards. The cone has a height of 2.4 yd. What is the diameter of the cone to the nearest tenth of a yard?

To find the diameter of the cone, we need to 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 of the cone,
π is a mathematical constant (approximately equal to 3.14159),
r is the radius of the base of the cone, and
h is the height of the cone.

In this case, we are given the volume (V) as 8.1 cubic yards and the height (h) as 2.4 yards, and we need to find the diameter (d) to the nearest tenth of a yard.

Since the radius (r) is half the diameter (d), we can rewrite the formula as:

V = (1/3) * π * (d/2)^2 * h

Substituting the given values:

8.1 = (1/3) * 3.14159 * (d/2)^2 * 2.4

To solve for d, we can rearrange the equation as follows:

(d/2)^2 = (8.1 * 3) / (3.14159 * 2.4)

Simplifying:

(d/2)^2 = 6.9

Now, let's find the square root of both sides:

d/2 = √6.9

d = 2 * √6.9

Calculating the value:

d ≈ 5.91 yards

Therefore, the diameter of the cone, rounded to the nearest tenth of a yard, is approximately 5.9 yards.