Answer:
48.9 ft³
Step-by-step explanation:
Volume of a cone can be determined by
V= πr² h/3
where
radius 'r' = 3feet
But we need to find height 'h'
If you see the figure in the attachment, the triangle is right angle.
Where,
slant height is hypotenuse
radius is base
height is perpendicular
Therefore, by using Pythagoras theorem
6² = 3² + h²
h² = 36 -9 = 27
h = √(27) = 3√3
Put the value of h in Volume of cone equation.
V= π3² (3√3) / 3
V=48.9 ft³
Therefore, The volume of this cone is 48.91ft³
Answer:
The volume of this cone is 48.91 cubic feet.
Step-by-step explanation:
In order to calculate the volume of this cone we need to use the appropriate formula as shown bellow:
Volume = (1/3)*pi*r²*h
But we have the slant height of the cone and not the height needed, in order to calculate that that we must use Pytagora's theorem, where the slant height is the hypothenuse, the radius of the base is one of the cathetus and the height of the cone is the other so we have:
6² = 3² + h²
h² = 36 -9 = 27
h = sqrt(27) = 3*sqrt(3)
So the volume is:
Volume = (1/3)*pi*(3)²*3*sqrt(3) = pi*9*sqrt(3) = 9*1.73*pi
Volume = 15.57*3.14159 = 48.91 cubic feet.
The volume of this cone is 48.91 cubic feet.
