Question

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

The surface area of the cone peak is approximately 439.2 square inches.

Step-by-step explanation:

To find the surface area of the cone peak, we need to find the lateral surface area of the cone. The lateral surface area of a cone can be found using the formula:

Lateral Surface Area = π * r * slant height

Using the given diameter of 14 inches, we can find the radius as half of the diameter, which is 7 inches. Plugging in the values into the formula, we get:

Lateral Surface Area = 3.14 * 7 * 20 = 439.2 square inches (rounded to the nearest hundredth)

Therefore, the surface area of the cone peak is approximately 439.2 square inches.

Answer 2

The given dimensions lead to a surface area of 439.60 square inches when rounded to the nearest hundredth.

Step-by-step explanation:

The student's question asks about the surface area of a cone with a given diameter and slant height. To determine the surface area of the cone peak, we need to calculate the lateral or side surface area because the cone does not have a base in this context. To find the surface area of the cone peak, calculate the lateral surface area with the formula πrl where r is the radius and l is the slant height. The formula for the lateral surface area of a cone is πrl where r is the radius and l is the slant height. Since the diameter is given as 14 inches, the radius r will be half of that, which is 7 inches. Using the given slant height l of 20 inches, we plug these into the formula.

Lateral Surface Area = πrl = 3.14 * 7 inches * 20 inches = 3.14 * 140 inches² = 439.6 inches². Rounding to the nearest hundredth, the surface area of the cone peak is 439.60 square inches.