A cylinder has a circular base with an area of 40 cm2 and a height of 60 cm. Determine the volume of a cone that has five times the radius and six times the height of the cylinder.

Step 1: Find the radius of the cylinder

The area of a circle is given by the formula A = πr², where r is the radius. We can rearrange this formula to solve for r: r = sqrt(A/π). Substituting the given area of 40 cm², we get r = sqrt(40/π) ≈ 3.57 cm.

Step 2: Determine the radius and height of the cone

The problem states that the cone has five times the radius and six times the height of the cylinder. Therefore, the radius of the cone is 5 * 3.57 cm = 17.85 cm, and the height of the cone is 6 * 60 cm = 360 cm.

Step 3: Calculate the volume of the cone

The volume V of a cone is given by the formula V = 1/3πr²h, where r is the radius and h is the height. Substituting the values we found for the radius and height of the cone, we get V = 1/3π * (17.85 cm)² * 360 cm ≈ 107,000 cm³.

Step 1: Find the radius of the cylinder

The area of a circle is given by the formula A = πr², where r is the radius. We can rearrange this formula to solve for r: r = sqrt(A/π). Substituting the given area of 40 cm², we get r = sqrt(40/π) ≈ 3.57 cm.

Step 2: Determine the radius and height of the cone

The problem states that the cone has five times the radius and six times the height of the cylinder. Therefore, the radius of the cone is 5 * 3.57 cm = 17.85 cm, and the height of the cone is 6 * 60 cm = 360 cm.

Step 3: Calculate the volume of the cone

The volume V of a cone is given by the formula V = 1/3πr²h, where r is the radius and h is the height. Substituting the values we found for the radius and height of the cone, we get V = 1/3π * (17.85 cm)² * 360 cm ≈ 107,000 cm³.