Question

Help its due in 5 hours. And I haven’t got the answer right for 2 hours.

Answer 1

$\text{Volume=}12.41n^2inches^3$

Explanation

the volume of a cone is given by:

$\text{Volume}=\frac{1}{3}\pi\cdot r^2\cdot h$

Step 1

find the radius:

let

Circumference= 6n inches

radius= r

$\begin{gathered} \text{Circumference = 2 }\cdot\pi\cdot radius \\ \text{replace} \\ 6n\text{ inches=2}\cdot\pi\cdot\text{ r} \\ \text{divide both sides by 2}\pi \\ \frac{6n\text{ }}{2\pi}\text{=}\frac{\text{2}\cdot\pi\cdot\text{ r}}{2\pi} \\ so \\ r=\frac{6n\text{ }}{2\pi}=\frac{3n}{\pi} \\ r=\frac{3n}{\pi} \end{gathered}$

Step 2

apply the formula for the volume of the cone:

let

h=13 inhces

$\begin{gathered} r=\frac{3n}{\pi} \\ h=13\text{ inches} \end{gathered}$

replace.

$\begin{gathered} \text{Volume}=\frac{1}{3}\pi\cdot r^2\cdot h \\ \text{Volume}=\frac{1}{3}\pi\cdot(\frac{3\text{ n}}{\pi})^2\cdot13 \\ \text{Volume}=\frac{1}{3}\pi\frac{(9n^2)}{\pi^2}\cdot13 \\ \text{Volume}=\frac{3n^2}{\pi}\cdot13 \\ \text{Volume}=\frac{39n^2}{\pi}in^3 \end{gathered}$

so, the answer is

$\begin{gathered} \text{Volume}=\frac{39n^2}{\pi}in^3 \\ \text{Volume}\approx\frac{39n^2}{\pi}in^3 \\ \text{Volume=}12.41n^2inches^3 \end{gathered}$

I hope this helps you