Answer:
Height of the cone = 4 m
Step-by-step explanation:
Given:
Volume of a cube = (12π) m^3
Radius of the cone = (6/2) m = 3 m
We have to find the value of "x".
And "x" is the height of the cone from the figure shown.
Formula to be used:
Volume of the cone: 1/3(πr^2h)
Here height = "x"
⇒ [tex]V_c_o_n_e=\frac{\pi r^2 h}{3}[/tex]
⇒ [tex]V_c_o_n_e=\frac{\pi r^2 x}{3}[/tex]
⇒ [tex]3\times V_c_o_n_e=\frac{\pi r^2 x}{3}\times 3[/tex]
⇒ [tex]3\times V_c_o_n_e=\pi r^2 x[/tex]
⇒ [tex]\frac{3\times V_c_o_n_e}{\pi r^2} =\frac{\pi r^2\times x}{\pi r^2}[/tex]
⇒ [tex]x=\frac{3\times V_c_o_n_e}{\pi r^2 }[/tex]
⇒ [tex]x=\frac{3\times 12\pi }{\pi (3)^2 }[/tex]
⇒ [tex]x=\frac{36\pi }{9\pi }[/tex]
⇒ [tex]x=\frac{36}{9}[/tex]
⇒ [tex]x=4[/tex] meters.
The height of the cone "x" = 4 meters option A is the right choice.
