To create 25 sacos de confeitar, approximately 31,972.50 cm² of wax paper is needed, which is calculated by finding the slant height using the Pythagorean theorem and then the lateral surface area of the cone.
The student is asking how much paper-manteiga (wax paper) will be needed to create 25 piping bags for cake decoration, using the shape of a right circular cone without a top, with given dimensions. We are provided with the height of the cone (20 cm) and the radius of the base (16 cm). Using the value of π (pi) as 3.14, we need to calculate the lateral surface area of one cone, which is equivalent to the area of a sector of a circle.
The formula for the lateral surface area (or slant height) of a cone is L = π * r * l, where r is the radius and l is the slant height of the cone. To find the slant height (l), we can use the Pythagorean theorem since we have a right cone: l = √(r² + h²) where r is the radius and h is the height of the cone.
First, calculate the slant height (l):
l = √(16² + 20²) = √(256 + 400) = √656 ≈ 25.61 cm
Next, calculate the lateral surface area of one cone (L):
L = 3.14 * 16 cm * 25.61 cm ≈ 1,278.90 cm²
Then, calculate the total paper required for 25 cones:
Total area = 25 * 1,278.90 cm² = 31,972.50 cm².
Thus, to create 25 sacos de confeitar, approximately 31,972.50 cm² of wax paper is required.