What is the area of the irregular shape of a cone if the radius is 7in and the height is 22in?
To find the area of the irregular shape of a cone, we need to calculate the lateral surface area of the cone.
The formula for the lateral surface area of a cone is A = πrℓ, where A represents the lateral surface area, r is the radius of the base, and ℓ denotes the slant height.
To find the slant height, we can use the Pythagorean theorem. The slant height can be determined using the formula ℓ = √(r^2 + h^2), where h is the height of the cone.
First, let's calculate the slant height:
ℓ = √(7^2 + 22^2)
= √(49 + 484)
= √533
≈ 23.09 in (rounded to two decimal places)
Now, we can use the formula for the lateral surface area of a cone:
A = πrℓ
= π * 7 * 23.09
≈ 505.29 in^2 (rounded to two decimal places)
Therefore, the area of the irregular shape of the cone is approximately 505.29 square inches.