Question

Calculate the volume of the cone slant height 25 radius 15

Answer 1

The volume of cone is 125600.

Step-by-step Step-by-step explanation :

GIVEN :

• 
  `\pink\star` Slant height of cone = 25
• 
  `\pink\star` Radius of cone = 15

TO FIND :

• 
  `\pink\star` Volume of cone

USING FORMULAS :

`\dashrightarrow{\sf{{(l)}^(2) = {(r)}^(2) + {(h)}^(2)}}`

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

• 
  `\purple\star` l = slant height
• 
  `\purple\star` V = volume
• 
  `\purple\star` π = 3.14
• 
  `\purple\star` r = radius
• 
  `\purple\star` h = height

SOLUTION :

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

`\begin{gathered} \qquad{\dashrightarrow{\sf{{(l)}^(2) = {(r)}^(2) + {(h)}^(2)}}} \\ \\\qquad{\dashrightarrow{\sf{{(25)}^(2) = {(15)}^(2) + {(h)}^(2)}}} \\ \\ \qquad{\dashrightarrow{\sf{(625) = (225)+ {(h)}^(2)}}} \\ \\ \qquad{\dashrightarrow{\sf{{(h)}^(2) = 625 - 225}}} \\ \\ \qquad{\dashrightarrow{\sf{{(h)}^(2) = 400}}} \\ \\ \qquad{\dashrightarrow{\sf{h = √(400)}}} \\ \\ \qquad{\dashrightarrow{\sf{\underline{\underline{h = 20}}}}} \end{gathered}`

Hence, the height of cone is 20.

`\rule{200}2`

Now, calculating the volume of cone by substituting all the given values in the formula :

`\begin{gathered} \qquad{\dashrightarrow{\sf{V_((Cone)) = (1)/(3) \pi {r}^(3)h}}} \\ \\ \qquad{\dashrightarrow{\sf{V_((Cone)) = (1)/(3) * 3.14 * {(20)}^(3) * 15}}} \\ \\ \qquad{\dashrightarrow{\sf{V_((Cone)) = 3.14 * {(20)}^(3) * 5}}} \\ \\ \qquad{\dashrightarrow{\sf{V_((Cone)) = 3.14 * 8000 * 5}}} \\ \\ \qquad{\dashrightarrow{\sf{V_((Cone)) = 15.7* 8000}}} \\ \\ \qquad{\dashrightarrow{\sf{\underline{\underline{V_((Cone)) = 125600}}}}}\end{gathered}`

Hence, the volume of cone is 125600.

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