# A cone has a height of #27 cm# and its base has a radius of #12 cm#. If the cone is horizontally cut into two segments #15 cm# from the base, what would the surface area of the bottom segment be?

Total surface area of bottom segment is

The cone is cut at 15 cm from base, So upper radius of the frustum

Total surface area of bottom segment is

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To find the surface area of the bottom segment of the cone, we need to calculate the area of the circular base of the cone and the lateral surface area of the segment.

First, let's find the slant height (l) of the cone:

l = √(h^2 + r^2) = √(27^2 + 12^2) = √(729 + 144) = √873 ≈ 29.54 cm

Next, we find the radius (R) of the segment formed by the horizontal cut:

R = r * (h - d) / h = 12 * (27 - 15) / 27 = 12 * 12 / 27 ≈ 5.33 cm

Now, we can calculate the lateral surface area (A_segment) of the segment using the formula:

A_segment = π * (R + r) * l

= π * (5.33 + 12) * 29.54 ≈ 1340.24 cm²

Therefore, the surface area of the bottom segment of the cone is approximately 1340.24 square centimeters.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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