Respuesta :
Answer:
- 40 units
Step-by-step explanation:
In the question, it is given that a right cone has a radius of 15 units and volume of 3000π 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}^{2}h ={ Volume_{(cone) }}}}}}}}} \\ \\[/tex]
Where,
- r refers to the radius of the cone.
- 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 {(15)}^{2} \times h = 3000 \pi}}}}}}} \\ \\[/tex]
Cancelling π from both sides we get :
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \cancel\pi \times {(15)}^{2} \times h = 3000 \cancel\pi}}}}}}} \\ \\[/tex]
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times 225 \times h = 3000}}}}}}} \\ \\[/tex]
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{225}{3} \times h = 3000}}}}}}} \\ \\[/tex]
[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf 75 \times h = 3000}}}}}} \\ \\[/tex]
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf h = \frac{3000}{75} }}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { h =40 }}}}}}} \\ \\[/tex]
Therefore,
- The height of the cone is 40 units .
