Respuesta :
Answer:
The volume of the sculpture is 53.589 ft³
Step-by-step explanation:
Here, we note that the volume of a right circular cone is given by
[tex]V = \pi r^2\frac{h}{3}[/tex]
Where:
V = Volume of the right circular cone
r = Radius of the base of the cone
h = Height of the cone = 5 ft
π = Constant = 3.14
However, the circumference is given as
Circumference = 20.096 ft
The formula for circumference is
Circumference = 2πr
Therefore, 2πr = 20.096 ft and
[tex]r = \frac{20.096 ft}{2\times \pi } = \frac{20.096 ft}{2\times 3.14}=3.2\, ft[/tex]
Therefore,
[tex]V = \pi r^2\frac{h}{3} = 3.14 \times 3.2^2 \times\frac{5}{3} = 53.589 \, ft^3[/tex].
Answer:
V = 53.5893 ft^3 .... (= 53.6 ft^3)
Step-by-step explanation:
Given:-
- The height of cone, h = 5 ft
- The circumference of base, c = 20.096 ft
Find:-
What is the volume of the cone-shaped sculpture?
Solution:-
- The volume of a cone (V) is given by:
V = pi/3*r^2*h
Where, r = radius of circular base
- To determine (r) we will use the formula for the circular base:
c = 2*pi*r
r = 20.096 / 2*3.14
r = 3.2 ft
- Now evaluate the volume V:
V = 3.14/3 * (3.2)^2 * 5
V = 53.5893 ft^3 .... (= 53.6 ft^3)
