Question

Hi , I have attached the question in the image, also there can be more than one answer.

Answer 1

Given:

The radius of the cone is given as r.

The height of the cone is given as h = 3r.

The objective is to find the volume of the cone.

Step-by-step explanation:

The general formula for the volume of a cone is,

`V=(1)/(3)\pi r^2h\text{ . . . . . .(1)}`

Substitute the value of h in the equation (1),

`\begin{gathered} V=(1)/(3)\pi r^2(3r) \\ V=\pi r^3\text{ . . . . . .(2)} \end{gathered}`

On solving the equation of height given in the figure in terms of radius,

`\begin{gathered} h=3r \\ r=(h)/(3)\text{ . . . . .(3)} \end{gathered}`

Substitute the equation (3) in equation (2),

`\begin{gathered} V=\pi((h)/(3))^3 \\ V=\pi(h^3)/(27)\text{ . . . . . .(4)} \end{gathered}`

Thus, both equation (2) and equation (4) are the volumes of the cone.

Hence, options (1) and (3) are the correct answers.