EXPLANATION:
Given;
We are given the dimensions of a cone shaped sculpture as follows;
[tex]\begin{gathered} Height=5ft \\ Base\text{ }circumference=28.260ft \end{gathered}[/tex]
Required;
We are required to find the volume of this cone-shaped sculpture.
Step-by-step solution;
To calculate the volume of a cone, the formula to be used is;
[tex]\begin{gathered} Volume\text{ }of\text{ }a\text{ }cone: \\ Vol=\pi r^2\frac{h}{3} \end{gathered}[/tex]
To determine the value of r, w shall take the variable r and make it the subject of the formula;
[tex]\begin{gathered} Circumference\text{ }of\text{ }a\text{ }circle: \\ Cir=2\pi r \\ make\text{ }r\text{ }the\text{ }subject: \\ \frac{C}{2\pi}=\frac{2\pi r}{2\pi} \\ \\ Therefore: \\ \frac{C}{2\pi}=r \end{gathered}[/tex]
With the value of the circumference already given we now have;
[tex]\begin{gathered} \frac{28.260}{2(3.14)}=r \\ \\ \frac{28.260}{6.28}=r \\ \\ 4.5=r \end{gathered}[/tex]
This means the radius of the circular base of the sculpture is 4.5 feet.
The volume of the sculpture therefore is;
[tex]Vol=\pi r^2\frac{h}{3}[/tex][tex]\begin{gathered} Volume=3.14\times(4.5)^2\times\frac{5}{3} \\ \\ Volume=\frac{3.14\times20.25\times5}{3} \\ \\ Volume=105.975 \end{gathered}[/tex]
The volume rounded to the nearest hundredth therefore is,
ANSWER:
[tex]Volume=105.98ft^3[/tex]
