answer:To find the surface area of a cone, we need to calculate the area of the base (circle) and the lateral surface area (the curved part of the cone). The formula for the surface area of a cone is: Surface Area = πr² + πr * l where r is the radius, and l is the slant height of the cone. First, we need to find the slant height (l) using the Pythagorean theorem, since we have a right triangle formed by the height (h), radius (r), and slant height (l): l² = r² + h² Given the radius (r) is 5 cm and the height (h) is 12 cm: l² = (5 cm)² + (12 cm)² l² = 25 cm² + 144 cm² l² = 169 cm² l = √169 cm² l = 13 cm Now we can find the surface area: Surface Area = π(5 cm)² + π(5 cm)(13 cm) Surface Area = 25π cm² + 65π cm² Surface Area = 90π cm² To round the answer to two decimal places, we can approximate π as 3.14: Surface Area ≈ 90 * 3.14 cm² Surface Area ≈ 282.6 cm² So, the surface area of the cone is approximately 282.6 cm².

answer:To find the surface area of a cone, we need to calculate the area of the base (a circle) and the lateral area (a sector of a circle), and then add them together. 1. Base area (A_base): A_base = π * r^2 A_base = π * (5 cm)^2 A_base = 25π cm^2 2. Lateral area (A_lateral): First, we need to find the height (h) of the cone using the Pythagorean theorem, since we have the slant height (l) and the radius (r). h = √(l^2 - r^2) h = √(12^2 - 5^2) h = √(144 - 25) h = √119 cm Now, we can find the lateral area using the formula: A_lateral = π * r * l A_lateral = π * (5 cm) * (12 cm) A_lateral = 60π cm^2 3. Total surface area (A_total): A_total = A_base + A_lateral A_total = 25π cm^2 + 60π cm^2 A_total = 85π cm^2 The surface area of the cone is 85π cm^2, or approximately 267.04 cm^2.

answer:To find the total surface area of a cone, we need to calculate the lateral surface area and the base area, and then add them together. The formula for the lateral surface area of a cone is: Lateral Surface Area = π * r * l where r is the radius and l is the slant height. The formula for the base area of a cone is: Base Area = π * r^2 Plugging in the given values, we have: Lateral Surface Area = π * 5 cm * 10 cm = 50π cm² Base Area = π * (5 cm)^2 = 25π cm² Now, we add the lateral surface area and the base area to find the total surface area: Total Surface Area = Lateral Surface Area + Base Area Total Surface Area = 50π cm² + 25π cm² = 75π cm² So, the total surface area of the cone is 75π cm².

answer:To find the surface area of a cone, we use the formula: Surface Area = πr(r + l) where r is the radius of the base, and l is the slant height of the cone. First, we need to find the slant height using the Pythagorean theorem: l = √(r^2 + h^2) where h is the height of the cone. Plugging in the given values: l = √(6^2 + 10^2) = √(36 + 100) = √136 Now, we can find the surface area: Surface Area = π(6)(6 + √136) ≈ 3.14(6)(6 + 11.66) ≈ 3.14(6)(17.66) ≈ 334.93 cm² So, the surface area of the cone is approximately 334.93 cm², rounded to the nearest hundredth.