Question

Find the volume of the cone

Answer 1

The volume of cone is 476.61 cm³.

Step-by-step explanation:

Solution :

As per given question we have provided :

• 
  `\green\star` Slant height = 14 cm
• 
  `\green\star` Radius = 6 cm

`\begin{gathered}\end{gathered}`

Firstly, finding the height of cone by substituting the values in the formula :

`{\longrightarrow{\pmb{\sf{l = \sqrt{(r)^(2) + {(h)}^(2) }}}}}`

• 
  `\orange\star` Slant height (l) = 14 cm
• 
  `\orange\star` Radius (r) = 6 cm
• 
  `\orange\star` Height (h) = ?

Substituting all the given values in the formula to find the height of cone :

`\begin{gathered}\begin{array}{l}\quad{\longrightarrow{\sf{l = \sqrt{(r)^(2) + {(h)}^(2)}}}}\\\\\quad{\longrightarrow{\sf{{(l)}^(2) =(r)^(2) + {(h)}^(2)}}}\\\\\quad{\longrightarrow{\sf{{(14)}^(2) =(6)^(2) + {(h)}^(2)}}}\\\\\quad{\longrightarrow{\sf{{(14 * 14)} =(6 * 6) + {(h)}^(2)}}}\\\\\quad{\longrightarrow{\sf{{(196)} =(36) + {(h)}^(2)}}}\\\\\quad{\longrightarrow{\sf{ {(h)}^(2) = 196 - 36}}}\\\\\quad{\longrightarrow{\sf{ {(h)}^(2) = 160}}}\\\\\quad{\longrightarrow{\sf{h = √(160)}}}\\\\\quad{\longrightarrow{\sf{h = 12.65}}}\\\\\quad{\star{\underline{\boxed{\sf{\purple{h = 12.65}}}}}} \end{array}\end{gathered}`

Hence, the height of cone is 12.65 cm.

`\begin{gathered}\end{gathered}`

Now, finding the volume of cone by substituting the values in the formula :

`\longrightarrow{\pmb{\sf{V_((Cone)) = (1)/(3)\pi{r}^(2)h}}}`

• 
  `\orange\star` V = Volume
• 
  `\orange\star` π = 3.14
• 
  `\orange\star` r = radius
• 
  `\orange\star` h = height

Substituting all the given values in the formula to find the volume of cone :

`\begin{gathered}\begin{array}{l}\quad\longrightarrow{\sf{Volume_((Cone)) = (1)/(3)\pi{r}^(2)h}}\\\\\quad\longrightarrow{\sf{Volume_((Cone)) = (1)/(3) * 3.14{(6)}^(2) 12.65}}\\\\\quad\longrightarrow{\sf{Volume_((Cone)) = (1)/(3) * 3.14{(6 * 6)}12.65}}\\\\\quad\longrightarrow{\sf{Volume_((Cone)) = (1)/(3) * 3.14{(36)}12.65}}\\\\\quad\longrightarrow{\sf{Volume_((Cone)) = \frac{1}{\cancel{3}}* 3.14 * \cancel{36}* 12.65}}\\\\\quad\longrightarrow{\sf{Volume_((Cone)) = 3.14 * 12 * 12.65}}\\ \\\quad\longrightarrow{\sf{Volume_((Cone)) = 476.61 \: {cm}^(3)}}\\\\\quad\star{\underline{\boxed{\sf{\pink{Volume_((Cone)) = 476.61 \: {cm}^(3)}}}}}\end{array}\end{gathered}`

Hence, the volume of cone is 476.61 cm³.

`\rule{300}{2.5}`

Answer 2

Explanation:

slant height l = 14cm

r = 6 cm

Use Pythagorean theorem.

h² + 6² = 14²

h² + 36 = 196

h² = 196 - 36

h² = 160

h = √160

h = 12.65 cm

`Volume=(1)/(3)\pi r^(2)h\\\\=(1)/(3)*3.14*6*6*12.64\\\\`

= 476.61 cubic cm