To find the surface area of a cone, we need to find the lateral surface area and the base area first.
The lateral surface area of a cone is given by the formula: L = πrℓ, where r is the radius of the base and ℓ is the slant height.
The slant height can be found using the Pythagorean theorem: ℓ = √(r^2 + h^2), where h is the height of the cone.
Given: r = 6 and h = 11
First, let's find the slant height:
ℓ = √(6^2 + 11^2) = √(36 + 121) = √157 ≈ 12.5 (rounded to the nearest tenth)
Next, let's calculate the lateral surface area:
L = πrℓ = 3.14 * 6 * 12.5 ≈ 235.5 (rounded to the nearest tenth)
The base area of a cone is given by the formula: B = πr^2
Next, let's calculate the base area:
B = π * 6^2 = 3.14 * 36 = 113.04 (rounded to the nearest hundredth)
The surface area of the cone is the sum of the lateral surface area and the base area:
Surface Area = L + B = 235.5 + 113.04 ≈ 348.5 (rounded to the nearest tenth)
Therefore, the surface area of the cone is approximately 348.5 square units.
what is the surface area of the cone? use 3.14 for pi and round to the nearest tenth, if necessary. height 11 radius 6
7 answers
@ExplainBot answer?
Apologies for the confusion in the previous response. Let's calculate the surface area of the cone again.
The surface area of a cone can be divided into two parts: the lateral surface area and the base area.
The lateral surface area (L) can be calculated using the formula: L = πrℓ, where r is the radius of the base and ℓ is the slant height.
The base area (B) can be calculated using the formula: B = πr^2, where r is the radius of the base.
Given: radius (r) = 6 and height (h) = 11
First, let's find the slant height (ℓ):
ℓ = √(r^2 + h^2) = √(6^2 + 11^2) = √(36 + 121) ≈ √157 ≈ 12.5 (rounded to the nearest tenth)
Now, let's calculate the lateral surface area (L):
L = πrℓ = 3.14 * 6 * 12.5 ≈ 235.5 (rounded to the nearest tenth)
Next, let's calculate the base area (B):
B = πr^2 = 3.14 * 6^2 = 3.14 * 36 ≈ 113.04 (rounded to the nearest hundredth)
The surface area of the cone is then the sum of the lateral surface area and the base area:
Surface Area = L + B = 235.5 + 113.04 ≈ 348.5 (rounded to the nearest tenth)
Therefore, the surface area of the cone is approximately 348.5 square units.
The surface area of a cone can be divided into two parts: the lateral surface area and the base area.
The lateral surface area (L) can be calculated using the formula: L = πrℓ, where r is the radius of the base and ℓ is the slant height.
The base area (B) can be calculated using the formula: B = πr^2, where r is the radius of the base.
Given: radius (r) = 6 and height (h) = 11
First, let's find the slant height (ℓ):
ℓ = √(r^2 + h^2) = √(6^2 + 11^2) = √(36 + 121) ≈ √157 ≈ 12.5 (rounded to the nearest tenth)
Now, let's calculate the lateral surface area (L):
L = πrℓ = 3.14 * 6 * 12.5 ≈ 235.5 (rounded to the nearest tenth)
Next, let's calculate the base area (B):
B = πr^2 = 3.14 * 6^2 = 3.14 * 36 ≈ 113.04 (rounded to the nearest hundredth)
The surface area of the cone is then the sum of the lateral surface area and the base area:
Surface Area = L + B = 235.5 + 113.04 ≈ 348.5 (rounded to the nearest tenth)
Therefore, the surface area of the cone is approximately 348.5 square units.
a cook wants to cover the side of a cone-shaped funnel with parchment paper to avoid any leaks or spills. the funnel has a diameter of 6 inches and a slant height of 4 inches. how many square inches of parchment paper is needed to cover the side of the funnel? use 3.14 for pi and round your answer to the nearest hundredth. (1point)
To find the surface area of the side of the funnel, we need to calculate the lateral surface area.
The lateral surface area of a cone is given by the formula: L = πrℓ, where r is the radius of the base and ℓ is the slant height.
Given: diameter = 6 inches, radius (r) = 6 / 2 = 3 inches, slant height (ℓ) = 4 inches.
Let's calculate the lateral surface area (L):
L = πrℓ = 3.14 * 3 * 4 = 37.68 (rounded to the nearest hundredth)
Therefore, the cook would need approximately 37.68 square inches of parchment paper to cover the side of the funnel.
The lateral surface area of a cone is given by the formula: L = πrℓ, where r is the radius of the base and ℓ is the slant height.
Given: diameter = 6 inches, radius (r) = 6 / 2 = 3 inches, slant height (ℓ) = 4 inches.
Let's calculate the lateral surface area (L):
L = πrℓ = 3.14 * 3 * 4 = 37.68 (rounded to the nearest hundredth)
Therefore, the cook would need approximately 37.68 square inches of parchment paper to cover the side of the funnel.
a waffle cone is in the shape of a cone with a slant height of 8 inches and a radius of 3 inches. a baker wants to know the surface area of the cone in order to cover the cone with melted chocolate. what is the surface area of the side of the cone in square inches? use 3.14 for pi and round your answer to the nearest hundredth. (1point)
To find the surface area of the side of the cone, we need to calculate the lateral surface area.
The lateral surface area of a cone is given by the formula: L = πrℓ, where r is the radius of the base and ℓ is the slant height.
Given: radius (r) = 3 inches and slant height (ℓ) = 8 inches.
Let's calculate the lateral surface area (L):
L = πrℓ = 3.14 * 3 * 8 = 75.36 (rounded to the nearest hundredth)
Therefore, the surface area of the side of the cone is approximately 75.36 square inches.
The lateral surface area of a cone is given by the formula: L = πrℓ, where r is the radius of the base and ℓ is the slant height.
Given: radius (r) = 3 inches and slant height (ℓ) = 8 inches.
Let's calculate the lateral surface area (L):
L = πrℓ = 3.14 * 3 * 8 = 75.36 (rounded to the nearest hundredth)
Therefore, the surface area of the side of the cone is approximately 75.36 square inches.
1 answer