a right circular cone with a radius of 4 feet and a height of 3 feet. Round to the nearest tenth what is the surface area?
A = πr(r+s)
where r^2 + h^2 = s^2
so plug in your numbers.
A = π*4(4+5) = 36π
Why did the circular cone go on a diet? It wanted to reduce its circumference!
But let's get back to your question. To find the surface area of a right circular cone, we need to calculate the area of its base and the area of its lateral surface.
The area of the base can be found using the formula for the area of a circle: A = πr^2, where r is the radius. In this case, the radius is 4 feet. So, the area of the base is A = π(4^2) = 16π square feet.
The lateral surface area can be found using the formula: A = πrl, where r is the radius 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. In this case, the slant height is l = √(4^2 + 3^2) = √(16 + 9) = √25 = 5 feet.
Now we can calculate the lateral surface area: A = π(4)(5) = 20π square feet.
Adding the area of the base and the lateral surface area, we get the total surface area:
Surface Area = 16π + 20π = 36π square feet.
Rounding to the nearest tenth, the surface area of the cone is approximately 113.1 square feet.
To find the surface area of a right circular cone, we need to sum the areas of the base and the lateral surface.
1. Base Area:
The base of the cone is a circle, and its area can be found using the formula A = πr^2, where r is the radius.
Given that the radius is 4 feet, we can calculate the base area:
A_base = π * 4^2
2. Lateral Surface Area:
The lateral surface of the cone forms a curved surface, which can be found using the formula A = πrℓ, where r is the radius, and ℓ is the slant height. The slant height can be calculated using the Pythagorean theorem as ℓ = √(r^2 + h^2), where h is the height.
Given that the height is 3 feet, we can calculate the slant height:
ℓ = √(4^2 + 3^2)
3. Surface Area:
To find the total surface area, we sum the base area and the lateral surface area:
Total Surface Area = Base Area + Lateral Surface Area
Let's calculate the surface area step by step:
Step 1: Calculate the base area.
A_base = π * 4^2
Step 2: Calculate the slant height.
ℓ = √(4^2 + 3^2)
Step 3: Calculate the lateral surface area.
A_lateral = π * 4 * ℓ
Step 4: Calculate the total surface area.
Total Surface Area = A_base + A_lateral
Now, let's calculate these values:
Step 1: Calculate the base area.
A_base = π * 4^2
A_base = π * 16
Step 2: Calculate the slant height.
ℓ = √(4^2 + 3^2)
ℓ = √(16 + 9)
ℓ = √25
ℓ = 5
Step 3: Calculate the lateral surface area.
A_lateral = π * 4 * ℓ
A_lateral = π * 4 * 5
A_lateral = 20π
Step 4: Calculate the total surface area.
Total Surface Area = A_base + A_lateral
Total Surface Area = π * 16 + 20π
Total Surface Area = 36π
To round to the nearest tenth, we can use the approximation 3.14159 for π.
Total Surface Area ≈ 36 * 3.14159
Total Surface Area ≈ 113.09724
Therefore, the surface area of the cone, rounded to the nearest tenth, is approximately 113.1 square feet.
To find the surface area of a right circular cone, you need to calculate the area of the base and the lateral surface area and then add them together.
1. Area of the base:
The base of a right circular cone is a circle with a radius of 4 feet. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Plugging in the values, the area of the base is A = π(4^2) = π(16) = 16π square feet.
2. Lateral surface area:
The lateral surface area of a cone can be found using the formula A = πrl, where A is the lateral surface area, r is the radius, and l is the slant height.
To find the slant height, you can use the Pythagorean theorem: l = √(r^2 + h^2), where h is the height.
Plugging in the values, the slant height is l = √(4^2 + 3^2) = √(16 + 9) = √25 = 5 feet.
Now, calculating the lateral surface area: A = π(4)(5) = 20π square feet.
3. Total surface area:
To get the total surface area, you add the area of the base and the lateral surface area.
Total surface area = Area of the base + Lateral surface area
Total surface area = 16π + 20π = 36π square feet.
Rounded to the nearest tenth, the surface area of the cone is approximately 113.1 square feet.