To find the surface area of a cone, we need to calculate both the lateral surface area and the base area.
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Calculate the radius: The diameter is given as 38, so the radius \( r \) is: \[ r = \frac{diameter}{2} = \frac{38}{2} = 19 \]
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Calculate the lateral surface area: The formula for the lateral surface area \( L \) of a cone is given by: \[ L = \pi r l \] where \( l \) is the slant height. Given \( l = 30 \), we substitute the values: \[ L = 3.14 \times 19 \times 30 \] \[ L = 3.14 \times 570 = 1781.8 \]
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Calculate the base area: The formula for the area of the base \( B \) of a cone is: \[ B = \pi r^2 \] So substituting the value of \( r \): \[ B = 3.14 \times 19^2 \] \[ B = 3.14 \times 361 = 1134.14 \]
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Calculate the total surface area: The total surface area \( SA \) is the sum of the lateral surface area and the base area: \[ SA = L + B \] \[ SA = 1781.8 + 1134.14 = 2915.94 \]
The surface area of the cone is approximately \( 2915.94 \) square units.
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