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Cone has diameter of 14 inches and slant height of 20 inches. Find the surface area to nearesth hundredth. Need units.
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no name
What are the units
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GPT 3.5
To find the surface area of a cone, we need to determine the lateral area and the base area.
The lateral area of a cone is given by the formula:
Lateral area = π * r * s,
where r is the radius of the cone and s is the slant height.
First, we need to find the radius, which is half the diameter. So, the radius is 14 inches / 2 = 7 inches.
Now, we can calculate the lateral area using the formula:
Lateral area = π * 7 inches * 20 inches
Lateral area ≈ 439.82 square inches (rounded to the nearest hundredth).
Next, we need to find the base area of the cone. The base is a circle with radius 7 inches.
Base area = π * (7 inches)^2
Base area ≈ 153.94 square inches (rounded to the nearest hundredth).
Finally, we can compute the surface area of the cone by adding the lateral and base areas:
Surface area = Lateral area + Base area
Surface area ≈ 439.82 square inches + 153.94 square inches
Surface area ≈ 593.76 square inches (rounded to the nearest hundredth).
Therefore, the surface area of the cone is approximately 593.76 square inches.
The lateral area of a cone is given by the formula:
Lateral area = π * r * s,
where r is the radius of the cone and s is the slant height.
First, we need to find the radius, which is half the diameter. So, the radius is 14 inches / 2 = 7 inches.
Now, we can calculate the lateral area using the formula:
Lateral area = π * 7 inches * 20 inches
Lateral area ≈ 439.82 square inches (rounded to the nearest hundredth).
Next, we need to find the base area of the cone. The base is a circle with radius 7 inches.
Base area = π * (7 inches)^2
Base area ≈ 153.94 square inches (rounded to the nearest hundredth).
Finally, we can compute the surface area of the cone by adding the lateral and base areas:
Surface area = Lateral area + Base area
Surface area ≈ 439.82 square inches + 153.94 square inches
Surface area ≈ 593.76 square inches (rounded to the nearest hundredth).
Therefore, the surface area of the cone is approximately 593.76 square inches.