A cone has a height of #7 cm# and its base has a radius of #2 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 the truncated cone is
Lateral surface area of full cone
Lateral Surface Area of top porion of the cut cone
Lateral Surface area of the truncated cone
Base area of full cone
Base area of top portion of the cut cone (top surface area of the frustum of the cone)
Total Surface Area of the truncated cone is
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To find the surface area of the bottom segment of the cone after it's horizontally cut 3 cm from the base, you can follow these steps:

Find the slant height of the bottom segment using the Pythagorean theorem: (l = \sqrt{r^2 + h^2}) (l = \sqrt{2^2 + 3^2}) (l = \sqrt{4 + 9}) (l = \sqrt{13}) cm

Find the radius of the bottom segment using similar triangles: (\frac{r_{\text{segment}}}{r_{\text{cone}}} = \frac{h_{\text{segment}}}{h_{\text{cone}}}) (\frac{r_{\text{segment}}}{2} = \frac{4}{7}) (r_{\text{segment}} = \frac{8}{7}) cm

Calculate the surface area of the bottom segment using the formula for the lateral surface area of a cone: (A_{\text{segment}} = \pi r_{\text{segment}} l) (A_{\text{segment}} = \pi \times \frac{8}{7} \times \sqrt{13}) square cm

Calculate the numerical value of the surface area of the bottom segment using a calculator.
Therefore, the surface area of the bottom segment of the cone would be approximately (28.18) square cm (rounded to two decimal places).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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