# A cone has a height of #9 cm# and its base has a radius of #4 cm#. If the cone is horizontally cut into two segments #7 cm# from the base, what would the surface area of the bottom segment be?

Total surface area of bottom segment is

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To find the surface area of the bottom segment of the cone, first calculate the slant height of the cone using the Pythagorean theorem:

Slant height (l) = √(radius^2 + height^2) = √(4^2 + 9^2) = √(16 + 81) = √97 ≈ 9.85 cm

Now, the surface area of the bottom segment (excluding the circular base) can be calculated using the formula:

Surface area = π * radius * slant height

Surface area = π * 4 * 9.85 ≈ 123.69 square centimeters

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