Eli is making a model castle out of clay. One of the roof peaks is in the shape of a cone with a diameter of 14 inches and a slant height of 20 inches. What is the surface area of the cone peak? Round your answer to the nearest hundredth. Use 3.14 for pi

Question

Illustrate an engaging and appealing scene featuring a young Caucasian boy named Eli. He is deeply engrossed in crafting a stunning model of a medieval castle using various shades of grey clay. Key details to emphasize include the castle's impressive scale, its intricate architectural features, and primarily, its distinctive roof peak, which assumes the form of a perfect cone. The cone should measure 14 inches across its base diameter and possess a slant height, extending from base to peak, of approximately 20 inches.

Eli is making a model castle out of clay. One of the roof peaks is in the shape of a cone with a diameter of 14 inches and a slant height of 20 inches. What is the surface area of the cone peak? Round your answer to the nearest hundredth. Use 3.14 for pi

Answer 1

To find the surface area of the cone peak, we need to find the lateral surface area.

The formula for the lateral surface area of a cone is π * r * l, where r is the radius of the base and l is the slant height.

The radius of the base is half of the diameter, so it is 14 inches/2 = 7 inches.

Using the formula, the lateral surface area of the cone peak is 3.14 * 7 inches * 20 inches = 439.2 square inches.

Rounded to the nearest hundredth, the surface area of the cone peak is 439.2 square inches.