GreenBeanGravy
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A cone has a volume V, radius r, and a height of 12 cm. A cone has the same height and 1/3 of the radius of the original cone. Write an expression for its volume.

Respuesta :

Answer:

Step-by-step explanation:

[tex]V=\pi r^2*12=12\pi r^2\\V_{1}=\pi (\frac{1}{3} r)^2*12=\frac{4}{3} \pi r^2\\if ~you~want~to~compare~the~volumes,then \\\\\frac{V_{1}}{V} =\frac{\frac{4}{3}\pi r^2}{12 \pi r^2 } =\frac{1}{9} \\or~V_{1}=\frac{1}{9} V[/tex]

Lanuel

An expression for the volume of this cone is equal to [tex]\frac{4}{9r_1^2} \pi \;cm^3[/tex]

Given the following data:

Height of cone = 12 cm.

Radius, [tex]r_2[/tex] = [tex]\frac{1}{3} r_1[/tex] cm.

How to calculate the volume.

Mathematically, the volume of a cone is given by this formula:

[tex]V = \frac{1}{3} \pi r^2h[/tex]

Where:

  • h is the height.
  • r is the radius.

For cone 1:

[tex]V = \frac{1}{3} \times \pi r^2 \times 12\\\\V=4\pi r^2\;cm^3[/tex]

For cone 2:

[tex]V = \frac{1}{3} \times \pi (\frac{1}{3r_1} )^2 \times 12\\\\V=\frac{4}{9r_1^2} \pi \;cm^3[/tex]

Read more on radius here: brainly.com/question/21367171

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