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A cone has a height of #14 cm# and its base has a radius of #7 cm#. If the cone is horizontally cut into two segments #6 cm# from the base, what would the surface area of the bottom segment be?

Answer 1

Ella Armstrong

# T S A = 436.2322 cm^2#

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Answer 2

Sophia Alfred

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

[l = \sqrt{r^2 + h^2}] [l = \sqrt{7^2 + (14-6)^2}] [l = \sqrt{49 + 64}] [l = \sqrt{113}] [l ≈ 10.63 \text{ cm}]

Then, use the formula for the lateral surface area of a cone segment:

[A = \pi r l] [A = \pi \times 7 \times 10.63] [A ≈ 223.86 \text{ cm}^2]

So, the surface area of the bottom segment of the cone is approximately (223.86 \text{ cm}^2).

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Answer from HIX Tutor

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.