A cone has a height of $18 c m$ $18 cm$ and its base has a radius of $9 c m$ $9 cm$ . If the cone is horizontally cut into two segments $3 c m$ $3 cm$ from the base, what would the surface area of the bottom segment be?

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A cone has a height of $18 c m$ $18 cm$ and its base has a radius of $9 c m$ $9 cm$ . If the cone is horizontally cut into two segments $3 c m$ $3 cm$ from the base, what would the surface area of the bottom segment be?

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Answer 1 · 2017-09-21T00:45:45

Surface area $\approx 148.833 c m^{2}$ $~~148.833cm^2$

Explanation:

For a really detailed explanation of how to solve questions like these, check out my other similar answers at

https://socratic.org/questions/a-cone-has-a-height-of-16-cm-and-its-base-has-a-radius-of-3-cm-if-the-cone-is-ho-1#478093 and

https://socratic.org/questions/a-cone-has-a-height-of-16-cm-and-its-base-has-a-radius-of-8-cm-if-the-cone-is-ho-1#476669

$R_{2}$ $R_2$ equals
$\frac{18}{3} = \frac{3}{R_{2}}$ $18/3=3/R_2$
$18 R_{2} = 9$ $18R_2=9$
$R_{2} = \frac{9}{18} = \frac{1}{2} = 0.5$ $R_2=9/18=1/2=0.5$

$s$ $s$ equals
$s = \sqrt{{(3 - 0.5)}^{2} + 3^{2}}$ $s=sqrt((3-0.5)^2+3^2)$
$s = \sqrt{6.25 + 9}$ $s=sqrt(6.25+9)$
$s = \sqrt{15.25}$ $s=sqrt(15.25)$

Surface area equals
$A_{s} = π (\sqrt{15.25} (3 - 0.5) + 3^{2} + {0.5}^{2})$ $A_s=pi(sqrt15.25(3-0.5)+3^2+0.5^2)$
$A_{s} = π (38.125 + 9 + 0.25)$ $A_s=pi(38.125+9+0.25)$
$A_{s} = π (47.375)$ $A_s=pi(47.375)$
$A_{s} \approx 148.833 c m^{2}$ $A_s~~148.833cm^2$ ,
Therefore the surface area of the bottom cone segment is roughly 148.833 $c m^{2}$ $cm^2$ .

I hope I helped!

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A cone has a height of $18 c m$ $18 cm$ and its base has a radius of $9 c m$ $9 cm$ . If the cone is horizontally cut into two segments $3 c m$ $3 cm$ from the base, what would the surface area of the bottom segment be?

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A cone has a height of 18cm18 cm and its base has a radius of 9cm9 cm. If the cone is horizontally cut into two segments 3cm3 cm from the base, what would the surface area of the bottom segment be?

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A cone has a height of $18 c m$ $18 cm$ and its base has a radius of $9 c m$ $9 cm$ . If the cone is horizontally cut into two segments $3 c m$ $3 cm$ from the base, what would the surface area of the bottom segment be?