Answer:
V ≈ 340 cm³
Step-by-step explanation:
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (10, - 4)
d = [tex]\sqrt{(10+2)^2+(-4-1)^2}[/tex]
= [tex]\sqrt{12^2+(-5)^2}[/tex]
= [tex]\sqrt{144+25}[/tex] = [tex]\sqrt{169}[/tex] = 13
The volume (V) of a cone is calculated as
V = [tex]\frac{1}{3}[/tex]πr²h ( r is the radius and h the height )
here r = 5 and h = 13, thus
V = [tex]\frac{1}{3}[/tex]π × 5² × 13
= [tex]\frac{1}{3}[/tex]π × 25 × 13
= [tex]\frac{1}{3}[/tex]π × 325
= [tex]\frac{325\pi }{3}[/tex] ≈ 340 cm³
