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