Respuesta :

Space

Answer:

[tex]\displaystyle \boxed{ V = \frac{\pi r^3}{3} }[/tex]

General Formulas and Concepts:
Geometry

Volume Formula [Cone]: [tex]\displaystyle V = \frac{\pi r^2 h}{3}[/tex]

  • r is radius
  • h is height

Step-by-step explanation:

Step 1: Define

Identify given variables.

h = r

Step 2: Find Volume

  1. [Volume Formula - Cone] Substitute in variables:
    [tex]\displaystyle\begin{aligned}V & = \frac{\pi r^2 h}{3} \\& = \frac{\pi r^2 r}{3}\end{aligned}[/tex]
  2. Simplify:
    [tex]\displaystyle\begin{aligned}V & = \frac{\pi r^2 h}{3} \\& = \frac{\pi r^2 r}{3} \\& = \boxed{\frac{\pi r^3}{3}}\end{aligned}[/tex]

∴ we have found the volume of the cone in terms of its radius.

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Learn more about Geometry: https://brainly.com/question/27700776

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Topic: Geometry

The volume of the cone in terms of its radius is [tex]V=\frac{\pi r^{3} }{3}[/tex]

Volume of the cone

The volume of a cone is the space or capacity inside the cone. Volume  [tex]V=\frac{\pi r^{2} h}{3}[/tex]  

Where r is radius and h is height.

How to determine the volume of cone whose height is equal to its radius?

Here, h = r

then

Volume [tex]V=\frac{\pi r^{2} h}{3}[/tex]      

                  [tex]=\frac{\pi r^{2}r }{3}[/tex]  

                  [tex]=\frac{\pi r^{3} }{3}[/tex]

Thus, the volume of the cone in terms of its radius is [tex]=\frac{\pi r^{3} }{3}][/tex]

Learn more about volume of cone here: brainly.com/question/27700776

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