# A cone has a height of #12 cm# and its base has a radius of #15 cm#. If the cone is horizontally cut into two segments #3 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 after it's cut 3 cm from the base, we first need to calculate the slant height of the smaller cone formed by the cut. Using the Pythagorean theorem, we can find the slant height ( l ) of the smaller cone:

[ l = \sqrt{r^2 + h^2} ] [ l = \sqrt{15^2 + (12 - 3)^2} ] [ l = \sqrt{225 + 81} ] [ l = \sqrt{306} ] [ l ≈ 17.49 \text{ cm} ]

Now, we can calculate the lateral surface area of the smaller cone, which is the surface area of the bottom segment:

[ A = πr'l ] [ A = π(15)(17.49) ] [ A ≈ 2617.12 \text{ cm}^2 ]

Therefore, the surface area of the bottom segment of the cone after it's cut 3 cm from the base is approximately ( 2617.12 \text{ cm}^2 ).

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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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