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
