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The radius of the base of a right circular cone is 27 centimeters and its slant height is 38 centimeters.
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What, in terms of 𝜋, is its total surface area?
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The total surface area of a cone can be calculated by adding the base area to the area of the curved surface.
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As the base of a cone is a circle, we can calculate this area using the formula 𝜋𝑟 squared.
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We calculate the area of the curved surface using the formula 𝜋𝑟𝐿, where 𝐿 is the slant height of the cone.
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In our example, the radius of the base is 27 centimeters.
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Therefore, we can work out the base area by multiplying 𝜋 by 27 squared.
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27 squared is equal to 729.
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Therefore, the base area is 729𝜋.
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To calculate the area of the curved surface, we will use the formula 𝜋𝑟𝐿, where 𝑟 is the radius, in this case 27 centimeters, and 𝐿 is the slant height, 38 centimeters.
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27 multiplied by 38 is 1026.
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Therefore, the area of the curved surface is 1026𝜋.
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Adding 729𝜋 and 1026𝜋 gives us 1755𝜋.
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This means that the total surface area of a cone with radius 27 centimeters and slant height 38 centimeters is 1755𝜋.