Answer:
- The height of the cone is 4 inches.
Solution :
We are given a cylinder and a cone of same volume i.e
[tex] \longrightarrow[/tex] Volume of cone = Volume of cylinder
And also the diameter of the cylinder is given 4 inches
[tex] \longrightarrow[/tex] Radius = [tex]\sf \dfrac{Diameter}{2}[/tex]
[tex] \longrightarrow[/tex] Radius = [tex] \sf\dfrac{4}{2}[/tex]
[tex] \longrightarrow[/tex] Radius = 2 inches
The height of cylinder is 3 inches. And the diameter of the cone is 6 inches
[tex] \longrightarrow[/tex] Radius = [tex]\sf\dfrac{Diameter}{2} [/tex]
[tex] \longrightarrow[/tex] Radius = [tex] \sf\dfrac{6}{2}[/tex]
[tex] \longrightarrow[/tex] Radius = 3 inches
First, let us recall the Formulas of volume of cylinder and cone:
[tex] \quad\longrightarrow\quad \sf {Cone = \dfrac{1}{3}\pi r^2 h }[/tex]
[tex] \quad\longrightarrow\quad \sf {Cylinder = \pi r^2 h }[/tex]
Now, we know that the volume of cone is equal to the volume of cylinder
[tex] \implies\quad \sf{\dfrac{1}{3}\pi r^2 h = \pi r^2 h }[/tex]
On putting the values:
[tex] :\implies\quad \sf{\dfrac{1}{3}\pi \times 3^2 \times h = \pi \times 2^2 \times 3 }[/tex]
[tex] :\implies\quad \sf{\dfrac{1}{\cancel{3}}\times 3.14 \times\cancel{ 9 }\times h = 3.14 \times 4 \times 3 }[/tex]
[tex] :\implies\quad \sf{3.14 \times 3 \times h = 3.14 \times 12 }[/tex]
[tex]: \implies\quad \sf{ h = \dfrac{ \cancel{3.14} \times 12 }{ \cancel{3.14} \times 3} }[/tex]
[tex] :\implies\quad \sf{ h =\cancel{ \dfrac{12}{3}}}[/tex]
[tex] :\implies\quad \underline{\underline{\pmb{\sf{h = 4 inches }}} }[/tex]
ㅤㅤㅤㅤㅤ~Hence the height of the cone is 4 inches.
