What is the surface area of the given cone?
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What is the surface area of the given cone?
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Answer:
Step-by-step explanation:
To find the surface area of the given cone, we need to find the area of the base and the lateral area and add them together.
The base of the cone is a circle with radius 8 cm. So, the area of the base is:
A = πr^2
A = π(8 cm)^2
A = 64π cm^2
The lateral area of the cone is given by:
L = πrs
where r is the radius of the base and s is the slant height of the cone.
To find the slant height, we use the Pythagorean theorem:
s^2 = r^2 + h^2
s^2 = 8^2 + 15^2
s^2 = 289
s = 17 cm
So, the lateral area is:
L = π(8 cm)(17 cm)
L = 136π cm^2
Therefore, the total surface area of the cone is:
A = B + L
A = 64π cm^2 + 136π cm^2
A = 200π cm^2
A ≈ 628.32 cm^2
Therefore, the surface area of the given cone is approximately 628.32 square centimeters.
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