Eli is making a model castle out of clay. One of the roof peaks is in the shape of a cone with a diameter of 14 inches and a slant height of 20 inches. What is the surface area of the cone peak? Round your answer to the nearest hundredth.
To find the surface area of a cone, we need to calculate the area of the base and the lateral surface area.
The base of the cone is a circle, and its area can be calculated using the formula A = πr^2, where r is the radius of the base.
Given that the diameter of the base is 14 inches, the radius can be calculated by dividing the diameter by 2:
radius = 14 inches / 2 = 7 inches
Now we can calculate the area of the base:
A_base = πr^2 = π(7 inches)^2 ≈ 153.94 square inches (rounded to the nearest hundredth).
The lateral surface area of the cone can be calculated using the formula A_lateral = πrℓ, where ℓ is the slant height of the cone.
Given that the slant height is 20 inches, the lateral surface area is:
A_lateral = πrℓ = π(7 inches)(20 inches) ≈ 439.82 square inches (rounded to the nearest hundredth).
To find the total surface area of the cone peak, we add the area of the base and the lateral surface area:
A_total = A_base + A_lateral = 153.94 square inches + 439.82 square inches ≈ 593.76 square inches (rounded to the nearest hundredth).
Therefore, the surface area of the cone peak is approximately 593.76 square inches (rounded to the nearest hundredth).
To find the surface area of the cone peak, we need to calculate the lateral area and add it to the area of the base.
The formula for the lateral area of a cone is given by:
Lateral Area = π × radius × slant height
First, we need to find the radius of the cone peak. The diameter is given as 14 inches, so we can find the radius by dividing the diameter by 2:
Radius = diameter / 2 = 14 / 2 = 7 inches
Now, we can calculate the lateral area:
Lateral Area = π × radius × slant height = π × 7 × 20
Next, we need to find the area of the base. The base of the cone is a circle, and the formula for the area of a circle is given by:
Area of Circle = π × radius^2
Plugging in the radius we calculated earlier (7 inches), we can find the area of the base:
Area of Base = π × 7^2
To find the total surface area, we add the lateral area to the area of the base:
Surface Area = Lateral Area + Area of Base
Surface Area = π × 7 × 20 + π × 7^2
Now, we can calculate the numerical value of the surface area using the value of π as approximately 3.14:
Surface Area ≈ 3.14 × 7 × 20 + 3.14 × 7^2
Surface Area ≈ 439.92 + 153.86
Surface Area ≈ 593.78
Therefore, the surface area of the cone peak is approximately 593.78 square inches rounded to the nearest hundredth.
so what's the correct answer?
Wrong again!
SA = π rs, where s is the slant height, r is the radius
= π(7)(20) = appr 439.82 in^2