A cone has a height of $14 c m$ $14 cm$ and its base has a radius of $7 c m$ $7 cm$ . If the cone is horizontally cut into two segments $5 c m$ $5 cm$ from the base, what would the surface area of the bottom segment be?

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A cone has a height of $14 c m$ $14 cm$ and its base has a radius of $7 c m$ $7 cm$ . If the cone is horizontally cut into two segments $5 c m$ $5 cm$ from the base, what would the surface area of the bottom segment be?

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Answer 1 · 2017-10-11T20:33:11

Total surface area of the bottom segment = 419.6876 sq. cm.

Explanation:

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$\frac{r 1}{h 1} = \frac{r 2}{h 2}$ $(r1)/(h1)=(r2)/(h2)$
$\frac{7}{14} = \frac{r 2}{9}$ $7/14=(r2)/9$
$r 2 = \frac{9}{2}$ $r2=9/2$

$l 1 = \sqrt{{(r 1)}^{2} + {(h 1)}^{2}} = \sqrt{7^{2} + 14^{2}} = 7 \sqrt{5}$ $l1=sqrt((r1)^2+(h1)^2)=sqrt(7^2+14^2)=7sqrt5$
Lateral surface area of bigger one $= (π) \cdot r 1 \cdot l 1 = (\frac{22}{7}) \cdot 7 \cdot 7 \sqrt{5}$ $=(pi)*r1*l1=(22/7)*7*7sqrt5$
$= 154 \sqrt{5} = 344.3545$ $=154sqrt5=344.3545$

$l 2 = \sqrt{{(r 2)}^{2} + {(h 2)}^{2}} = \sqrt{{(\frac{9}{2})}^{2} + 9^{2}} = (\frac{9}{2}) \sqrt{5}$ $l2=sqrt((r2)^2+(h2)^2)=sqrt((9/2)^2+9^2)=(9/2)sqrt(5)$
Lateral surface area of smaller cone
$= (π) \cdot r 2 \cdot l 2$ $=(pi)*r2*l2$
$= \frac{22 \cdot 9 \cdot 9 \sqrt{5}}{7 \cdot 2 \cdot 2}$ $=(22*9*9sqrt5)/(7*2*2)$
$= (\frac{891}{14}) \sqrt{5} = 142.3098$ $=(891/14)sqrt5=142.3098$

Lateral surface area of the bottom segment
$= 344.3545 - 142.3098 = 202.0447$ $=344.3545-142.3098=202.0447$

Area of larger base $= \frac{22 \cdot 7 \cdot 7}{7} = 154$ $=(22*7*7)/7=154$

Area of smaller base $= \frac{22 \cdot 9 \cdot 9}{7 \cdot 2 \cdot 2} = \frac{891}{14} = 63.6429$ $=(22*9*9)/(7*2*2)=891/14=63.6429$

Surface area of the bottom segment
$= 202.0447 + 154 + 63.6429 = * 419.6876 *$ $=202.0447+154+63.6429= **419.6876**$ cm^2#

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A cone has a height of $14 c m$ $14 cm$ and its base has a radius of $7 c m$ $7 cm$ . If the cone is horizontally cut into two segments $5 c m$ $5 cm$ from the base, what would the surface area of the bottom segment be?

1 Answer

Explanation:

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A cone has a height of 14cm14 cm and its base has a radius of 7cm7 cm. If the cone is horizontally cut into two segments 5cm5 cm from the base, what would the surface area of the bottom segment be?

1 Answer

Explanation:

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A cone has a height of $14 c m$ $14 cm$ and its base has a radius of $7 c m$ $7 cm$ . If the cone is horizontally cut into two segments $5 c m$ $5 cm$ from the base, what would the surface area of the bottom segment be?