What is the slant height if the surface area is 395.64 square meters? (use 3.14 for π .) r = 7 of a cone a. 7 b. 9 c. 11 d. 13

1. The formula for calculate the area of a cone is:

 A=πr²+πrl  (1)

 A is the area (A=395.64 m²).
 π=3.14
 r is the radius (r=7).
 l is the height.

 2. The formula for calculate the slant height of the cone, is given by the Pythagorean theorem:

 h²=l²+r²
 h=√(l²+r²)   (2)

 h is the slant height.

 3. We don't know the value of "l", so:

 - We must rewrite the formula (1) and clear "l":

 A=πr²+πrl 
 A-πr²=πrl
 l=A-πr²/πr

 - Now, we must susbtitute l=A-πr²/πr, into the formula (2). Then, we have:

 h=√(l²+r²) 
 h=√[(A-πr²/πr)²+r²]

 A=395.64 m²
 π=3.14
 r=7

 4. When we substitute the values above into the formula h=√[(A-πr²/πr)²+r²], we obtain the slant height:
 
 h=√[(A-πr²/πr)²+r²]
 h=√170
 h=13 

 What is the slant height?

 The answer is: D.13