Question

Cones, Cylinders, & Spheres Unit Test 4 of 154 of 15 Items

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.(1 point)

square inches

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of a cone, we need to find the area of the curved surface (lateral area) and the area of the base.

The formula for the lateral area of a cone is given as: LA = πrℓ, where r is the radius and ℓ is the slant height.

Given that the diameter of the cone is 14 inches, we can calculate the radius by dividing the diameter by 2: r = 14/2 = 7 inches.

Using the given slant height of 20 inches, we can find the lateral area:

LA = 3.14 * 7 * 20 = 439.6 square inches.

The area of the base of the cone is calculated using the formula: A = πr^2.

A = 3.14 * 7^2 = 3.14 * 49 = 153.86 square inches.

To find the total surface area of the cone, we need to add the lateral area and the area of the base:

Surface Area = LA + A = 439.6 + 153.86 = 593.46 square inches.

Rounding to the nearest hundredth, the surface area of the cone peak is approximately 593.46 square inches.