Mathematics: What is the value of x if the volume of the cone is 12 pi m3

sup remember meStep-by-step explanation:...

What is the value of x if the volume of the cone

jocelynbarraza

25.01.2022

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"

⇒ $V_c_o_n_e=\frac{\pi r^2 h}{3}$

⇒ $V_c_o_n_e=\frac{\pi r^2 x}{3}$

⇒ $3\times V_c_o_n_e=\frac{\pi r^2 x}{3}\times 3$

⇒ $3\times V_c_o_n_e=\pi r^2 x$

⇒ $\frac{3\times V_c_o_n_e}{\pi r^2} =\frac{\pi r^2\times x}{\pi r^2}$

⇒ $x=\frac{3\times V_c_o_n_e}{\pi r^2 }$

⇒ $x=\frac{3\times 12\pi }{\pi (3)^2 }$

⇒ $x=\frac{36\pi }{9\pi }$

⇒ $x=\frac{36}{9}$

⇒ x=4 meters.

The height of the cone "x" = 4 meters option A is the right choice.

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