Question

Find the volume of this cone.

Answer 1

`\huge\text{Hey there!}`

`\huge\textbf{What is the formula for finding the}\\\\\huge\textbf{the volume of a cone?}`

`\large\boxed{\mathsf{(\pi * r^2* h)/(3) = volume}}`

`\bullet\large\textsf{ Whereas, \boxed{r} is your \underline{radius}, \boxed{h} is your \underline{height}, \& \boxed{\pi} is your pi.}`

`\bullet\large\textsf{The pi }\boxed{(\pi)}\large\textsf{ is approximately equal to 3.14.}`

`\huge\textbf{What are the labels in your equation?}`

`\star\ \large\boxed{{Radius}}\rightarrow \textsf{\underline{4\ centimeters}}}}}`

`\star\ \large\boxed{{Height}}\rightarrow \textsf{\underline{9\ centimeters}}}}}`

`\star\ \large\boxed{{\pi}}\rightarrow \textsf{\underline{3}}}}}`

`\huge\textbf{What does should the equation look}\\\\\huge\textbf{like?}`

`\large\boxed{\mathsf{(3 * 4^2 *9)/(3)}}`

`\huge\textbf{What are the steps to solve for the}\\\\\huge\textbf{question to get the result?}`

`\large\boxed{\mathsf{(3 * 4^2 *9)/(3)}}`

`\large\boxed{\mathsf{= (3*4*4*9)/(3)}}`

`\large\boxed{= \mathsf{(3*16*9)/(3)}}`

`\large\boxed{\mathsf{= (48*9)/(9)}}`

`\large\boxed{\mathsf{= (432)/(3)}}`

`\large\boxed{\mathsf{= (432 / 3)/(3/3)}}`

`\large\boxed{= \mathsf{(144)/(1)}}`

`\large\boxed{\mathsf{= 144/1}}`

`\large\boxed{= \textsf{144}}`

`\huge\textbf{What is the result to this question?}`

`\huge\boxed{\frak{144\ cm^3}}\huge\checkmark`

~

Answer 2

Calculate the volume of the cone

To start calculating the volume of the cone, we obtain the following data:

• r = 4 cm
• h = 9 cm
• π = 3

To calculate the volume of a cone, we apply the following formula:

`\boldsymbol{\sf{V=(\pi r^(2)h )/(3) }}`, where

• V = volume
• h = height
• r = radius
• π = pi

We solve, substituting our data in the formula:

• 
  `\boldsymbol{\sf{V=(3*(4 \ cm)^(2)*9 \ cm )/(3) }}`

taking the square root

• 
  `\boldsymbol{\sf{V=(3 *16 \ cm^(2)*9 \ cm )/(3) }}`

Multiplying

• 
  `\boldsymbol{\sf{V=(432 \ cm^(3) )/(3) }}`

Dividing

• 
  `\boxed{\boldsymbol{\sf{V=144 \ cm^(3) }}}`

Therefore the volume of the cone is 144 cm³.