Respuesta :

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Answer:

794.42 in²  (since I used the pi = 3.14159 , the result is slightly different,

Step-by-step explanation:

Formula: Given radius and slant height calculate the height, volume, lateral surface area and total surface area.  

Given r, s find h, V, L, A

h = √(s² - r²)

r = 11 in

h = 4.796 in

s = 12 in

V = 607.7 in³

L = 414.7 in²

B = 380.1 in²

A = 794.8 in

Agenda: r = radius

h = height

s = slant height

V = volume

L = lateral surface area

B = base surface area  

A = total surface area

π = pi = 3.14159

√ = square root

Answer:  the correct option is

(A) 794.42 in.²

Step-by-step explanation:  We are given to find the surface area of the cone shown in the figure.

We know that

the SURFACE AREA of a cone with height h units and radius r units is given by

[tex]S=\pi r(r+\sqrt{h^2+r^2}).[/tex]

For the given cone, we have

r = 11 in. and

[tex]h=\sqrt{12^2-11^2}=\sqrt{144-121}=\sqrt{23}=4.8.[/tex]

Therefore, the surface area of the given cone is

[tex]S\\\\=\pi r(r+\sqrt{h^2+r^2})\\\\=3.14\times11(11+\sqrt{4.8^2+11^2})\\\\=34.54(11+12)\\\\=34.54\times23\\\\=794.42.[/tex]

Thus, the required surface area of the given cone is 794.42 in.²

Option (A) is CORRECT.

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