A cook wants to cover the side of a cone-shaped funnel with parchment paper to avoid any leaks or spills. The funnel has a diameter of 6 inches and a slant height of 4 inches. How many square inches of parchment paper is needed to cover the side of the funnel? Use 3.14 for pi and round your answer to the nearest hundredth. (surface area cones practice question)
The circumference of the base of the cone is 6 inches. Using the formula for the circumference of a circle, we can find the radius of the base, which is half the diameter: 6 inches / 2 = 3 inches.
The slant height of the cone forms a right triangle with the height of the cone and the radius of the base. Using the Pythagorean theorem, we can find the height of the cone: h^2 = 4^2 - 3^2 = 16 - 9 = 7, so h = √7.
The lateral surface area of a cone is given by the formula π * r * l, where r is the radius of the base and l is the slant height. Plugging in the values, we get: 3.14 * 3 inches * 4 inches = 37.68 square inches.
Therefore, the cook would need approximately 37.68 square inches of parchment paper to cover the side of the funnel.