Answer:
The volume in terms of π is 144 ft³
The volume rounded to the nearest tenth is 452.4 ft³
Step-by-step explanation:
The formula of the volume of a cone is V = π r² h , where r is its radius and h is its height
The formula of the area of a circle is A = π r²
The area of the base of the cone is 36π ft²
Equate the formula of the area of the circle by 36π to find r
πr² = 36π
Divide both sides by π
r² = 36
Take √ to both sides
r = 6 ft
The height of the cone is equal to twice the radius
The radius of the cone is 6 ft
Multiply 6 by 2 to find the height
h = 2(6) = 12 ft
The height of the cone is 12 ft
Subsitute the values of h and r in the formula of the volume of the cone to find it
V = π(6)²(12)
V = 144 π ft³
V = 452.3893421 ft³
Round it to the nearest tenth
V = 452.4 ft³
