Question

The volume of a right cone is 168π units^3. If its diameter measures 12 units, find its height

Answer 1

• 14 units

Explanation:

In the question, it is given that a right cone has a diameter of 12 units and volume of 168π units³ and we have to find the height of the cone.

`\:`

To Find the height of the cone, we must know this formula :

`\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { (1)/(3) \: \pi r^2h ={ Volume_((cone) )}}}}}}}} \\ \\`

Where,

• r refers to the radius of the cone. Here, the diameter is 12, Therefore the radius will be 6 units.

• h refers to the height of the cone.

Now, we will substitute the values in the formula :

`\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { (1)/(3) * \pi * (6)^2 * h = 168 \pi}}}}}}} \\ \\`

Cancelling π from both sides we get :

`\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { (1)/(3) * \cancel\pi * 36 * h = 168 \cancel\pi}}}}}}} \\ \\`

`\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { (1)/(3) \ * 36 * h = 168 }}}}}}} \\ \\`

`\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { (36)/(3) * h = 168 }}}}}}} \\ \\`

`\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { 12 * h = 168 }}}}}}} \\ \\`

`\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { h = (168)/(12) }}}}}}} \\ \\`

`\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { h ={14 }}}}}}}} \\ \\`

Therefore,

• The height of the cone is 14 units .