Question

Please help me on this question! (Type an integer or decimal rounded to the nearest hundredth as needed)

Answer 1

Step-by-step explanation:

Given;

We are given the dimensions of a cone shaped sculpture as follows;

`\begin{gathered} Height=5ft \\ Base\text{ }circumference=28.260ft \end{gathered}`

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;

`\begin{gathered} Volume\text{ }of\text{ }a\text{ }cone: \\ Vol=\pi r^2(h)/(3) \end{gathered}`

To determine the value of r, w shall take the variable r and make it the subject of the formula;

`\begin{gathered} Circumference\text{ }of\text{ }a\text{ }circle: \\ Cir=2\pi r \\ make\text{ }r\text{ }the\text{ }subject: \\ (C)/(2\pi)=(2\pi r)/(2\pi) \\ \\ Therefore: \\ (C)/(2\pi)=r \end{gathered}`

With the value of the circumference already given we now have;

`\begin{gathered} (28.260)/(2(3.14))=r \\ \\ (28.260)/(6.28)=r \\ \\ 4.5=r \end{gathered}`

This means the radius of the circular base of the sculpture is 4.5 feet.

The volume of the sculpture therefore is;

`Vol=\pi r^2(h)/(3)`
`\begin{gathered} Volume=3.14*(4.5)^2*(5)/(3) \\ \\ Volume=(3.14*20.25*5)/(3) \\ \\ Volume=105.975 \end{gathered}`

The volume rounded to the nearest hundredth therefore is,

ANSWER:

`Volume=105.98ft^3`