Respuesta :
Answer:
- 14 units
Step-by-step 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.
[tex] \: [/tex]
To Find the height of the cone, we must know this formula :
[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { \dfrac{1}{3} \: \pi r^2h ={ Volume_{(cone) }}}}}}}}} \\ \\[/tex]
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 :
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \pi \times (6)^2 \times h = 168 \pi}}}}}}} \\ \\[/tex]
Cancelling π from both sides we get :
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \cancel\pi \times 36 \times h = 168 \cancel\pi}}}}}}} \\ \\[/tex]
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \ \times 36 \times h = 168 }}}}}}} \\ \\[/tex]
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{36}{3} \times h = 168 }}}}}}} \\ \\[/tex]
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { 12 \times h = 168 }}}}}}} \\ \\[/tex]
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { h = \frac{168}{12} }}}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { h ={14 }}}}}}}} \\ \\[/tex]
Therefore,
- The height of the cone is 14 units .
