Question

The cone shown has a radius of 6 inches and a slant height of 10 inches. What is the total surface area of the cone? Use 3.14 to approximate pi. Round your answer to the nearest whole.

Answer 1

To find the total surface area of the cone, we need to calculate the lateral surface area plus the area of the base.

The lateral surface area of a cone is π times the radius times the slant height. Given that π is approximately 3.14, the lateral surface area is:
Lateral surface area = π * radius * slant height
Lateral surface area = 3.14 * 6 * 10
Lateral surface area = 188.4 square inches

Next, we need to find the area of the base of the cone, which is a circle with radius 6 inches. The area of a circle is π times the square of the radius. Again, using an approximation of π as 3.14, the area of the base is:
Base area = π * radius^2
Base area = 3.14 * 6^2
Base area = 3.14 * 36
Base area = 113.04 square inches

Finally, the total surface area of the cone is the sum of the lateral surface area and the base area:
Total surface area = Lateral surface area + Base area
Total surface area = 188.4 + 113.04
Total surface area ≈ 301.44 square inches

Rounded to the nearest whole number, the total surface area of the cone is 301 square inches.