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The volume of the ice cream cone in the diagram is 12 cubic centimeters. 9 centimeters is the height of the ice cream cone, what is the diameter of the opening of the cone?​

The volume of the ice cream cone in the diagram is 12 cubic centimeters 9 centimeters is the height of the ice cream cone what is the diameter of the opening o class=

Respuesta :

karkismriti176

Answer:

2.2568m

Step-by-step explanation:

volume= 12 π cm³

or, 1/3 πr²h = 12π cm³

or, πr² × 9 = 12π ×3

or, r²= 36π/9π

or, r²= 4

or, r= 2

d = 2r = 2× 2= 4 cm

Lanuel

The diameter of the opening of the cone is equal to 4 centimeters.

Given the following data:

  • Volume of cone = 12π cubic centimeters.
  • Height of cone = 9 centimeters.

To determine the diameter of the opening of the cone:

How to calculate the diameter.

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.

Substituting the given parameters into the formula, we have;

[tex]12 \pi = \frac{1}{3} \pi r^2 \times 9\\\\12 =3r^2\\\\r^2=4\\\\r=\sqrt{4}[/tex]

r = 2 centimeters.

For the diameter:

[tex]Diameter = 2r\\\\Diameter = 2 \times 2[/tex]

Diameter = 4 centimeters.

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