If the surface area of the cone below is 628.32 m², find its volume. I WILL MARK BRAINLEIST IF CORRECT AND 20 POINTS

1586.91 m³

Step-by-step explanation:

From the diagram attached,

Applying,

A = πrl.................. Equation 1

Where A = surface area of the cone, l = slight heigth of the cone, π = pie.

make l the subject of the equation,

l = A/πr.............. Equation 2

From the question,

Given: A = 628.32 m², π = 3.14, r = 8 m

Substitite these values into equation 2

l = 628.32/(3.14×8)

l = 25 m

But,

l² = h²+r².................... Equation 3

Where h = height of the cone.

h = √(l²-r²)

h = √(25²-8²)

h = √(625-64)

h = √(561)

h = 23.69 m

Also Applying,

V = 1/3πr²h

Where V = volume of the cone.

Therefore,

V = (3.14×8²×23.69)/3

V = 1586.91 m³

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c