Find the volume of a right circular cone that has a height of 9.5 m and a base with a circumference of 10 m. Round your answer to the nearest tenth of a cubic meter.

Sure, let's solve this step by step.

Step 1: First, we need to find the radius of the base of the cone. We know that the circumference of a circle is given by the formula 2πr, where r is the radius of the circle. So, we can find the radius by rearranging this formula to r = circumference / (2π).

Given that the circumference is 10 m, we can substitute this into the formula to find the radius:

r = 10 m / (2π) ≈ 1.59 m

Step 2: Now that we have the radius, we can find the volume of the cone. The formula for the volume of a cone is (1/3)πr²h, where r is the radius and h is the height.

Substituting the radius and height into this formula gives:

Volume = (1/3)π * (1.59 m)² * 9.5 m ≈ 25.1 m³

So, the volume of the cone is approximately 25.1 cubic meters, rounded to the nearest tenth.

Sure, here are the steps to find the volume of a right circular cone:

Step 1: Find the radius of the base. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. We know that the circumference is 10 m, so we can set up the equation 10 = 2πr. Solving for r, we get r = 10 / (2π) ≈ 1.59 m.

Step 2: Use the formula for the volume of a cone. The formula is V = 1/3πr²h, where V is the volume, r is the radius, and h is the height. We know that r ≈ 1.59 m and h = 9.5 m, so we can substitute these values into the formula to get V = 1/3π(1.59)²(9.5) ≈ 25.1 m³.

So, the volume of the cone is approximately 25.1 cubic meters.