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`

Step-by-step explanation

the volume of a cone is given by:

`\text{Volume}=(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}=(3n)/(\pi) \\ r=(3n)/(\pi) \end{gathered}`

Step 2

apply the formula for the volume of the cone:

let

h=13 inhces

`\begin{gathered} r=(3n)/(\pi) \\ h=13\text{ inches} \end{gathered}`

replace.

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

so, the answer is

`\begin{gathered} \text{Volume}=(39n^2)/(\pi)in^3 \\ \text{Volume}\approx(39n^2)/(\pi)in^3 \\ \text{Volume=}12.41n^2inches^3 \end{gathered}`

I hope this helps you