A cone has a height of $8 c m$ $8 cm$ and its base has a radius of $4 c m$ $4 cm$ . If the cone is horizontally cut into two segments $4 c m$ $4 cm$ from the base, what would the surface area of the bottom segment be?

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Answer 1 · 2018-07-14T11:20:49

Total surface area of bottom segment is $147.13 (2 d p)$ $147.13 (2 dp)$ sq.cm

The cone is cut at $4$ $4$ cm from base, So upper radius of the

frustum of cone is $r_{2} = \frac{8 - 4}{8} \cdot 4 = 2$ $r_2=(8-4)/8*4=2$ cm ;

Slant height: $l = \sqrt{4^{2} + {(4 - 2)}^{2}} = \sqrt{20} \approx 4.47$ $l=sqrt(4^2+(4-2)^2)=sqrt20 ~~ 4.47$ cm

Top surface area $A_{t} = π \cdot 2^{2} \approx 12.57$ $A_t=pi*2^2~~ 12.57$ sq.cm

Bottom surface area $A_{b} = π \cdot 4^{2} \approx 50.27$ $A_b=pi*4^2~~50.27$ sq.cm

Slant Area $A_{s} = π \cdot l \cdot (r_{1} + r_{2}) = π \cdot 4.47 \cdot (4 + 2)$ $A_s=pi*l*(r_1+r_2)=pi*4.47*(4+2)$

$\approx 84.3$ $~~84.3$ sq.cm

Total surface area of bottom segment is ,

$A = A_{t} + A_{b} + A_{s} = 12.57 + 50.27 + 84.3 \approx 147.13 (2 d p)$ $A=A_t+A_b+A_s=12.57+50.27+84.3~~147.13 (2dp)$

sq.cm. [Ans]

A cone has a height of 8cm8 cm and its base has a radius of 4cm4 cm. If the cone is horizontally cut into two segments 4cm4 cm from the base, what would the surface area of the bottom segment be?