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An open cone has a radius of 6cm and a height of 8cm.what is the surface area in square centimeters
To find the surface area of an open cone, we need to calculate the lateral surface area.
The formula for the lateral surface area of a cone is given by:
Lateral Surface Area = π × r × ℓ
where r is the radius of the cone's base and ℓ is the slant height of the cone.
To find the slant height, we can use the Pythagorean theorem. The slant height (ℓ) is the hypotenuse of a right triangle formed by the height (h) and the radius (r) of the cone.
In this case, the height (h) is 8 cm, and the radius (r) is 6 cm.
Using the Pythagorean theorem, we can calculate the slant height (ℓ):
ℓ = √(r^2 + h^2)
ℓ = √(6^2 + 8^2)
ℓ = √(36 + 64)
ℓ = √100
ℓ = 10 cm
Now we can calculate the lateral surface area:
Lateral Surface Area = π × r × ℓ
Lateral Surface Area = π × 6 cm × 10 cm
Lateral Surface Area ≈ 188.5 cm^2
Therefore, the surface area of the open cone is approximately 188.5 square centimeters.