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The radius of the large sphere is 3 times longer than the radius of the small sphere.


How many times smaller than the volume of the large sphere is the volume of the small sphere?

Respuesta :

SociometricStar

Answer:

27 times

Step-by-step explanation:

Let the radius of the smaller sphere is x.

Then the radius of the larger sphere is 3x.

The volume of a sphere is given by

[tex]V=\frac{4}{3}\pi r^3[/tex]

Hence, the volume of the smaller sphere is [tex]V_1=\frac{4}{3}\pi x^3[/tex]

And the volume of the larger sphere is

[tex]V_2=\frac{4}{3}\pi (3x)^3\\\\V_2=\frac{4}{3}\pi 27x^3[/tex]

Divide both volumes, we get

[tex]\frac{V_1}{V_2}=\frac{\frac{4}{3}\pi x^3}{\frac{4}{3}\pi 27x^3}\\\\\frac{V_1}{V_2}=\frac{1}{27}\\\\V_2=27V_1[/tex]

Hence, the volume of the smaller sphere is 27 times smaller than the volume of the larger sphere.

The volume of the smaller sphere is 1/27 times of larger than the volume of the larger sphere.

What is a sphere?

It is defined as three-dimensional geometry when half-circle two-dimensional geometry revolved around the diameter of the sphere that will form.

[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]

The radius of the large sphere is 3 times longer than the radius of the small sphere.

R = 3r

The volume of the large sphere:

[tex]\rm V = \dfrac{4}{3} \pi (3r)^3[/tex]

The volume of the large sphere:

[tex]\rm v = \dfrac{4}{3} \pi (r)^3[/tex]

v/V = 1/27

V = 27v or

v = V/27

Thus, the volume of the smaller sphere is 1/27 times of larger than the volume of the larger sphere.

Learn more about the sphere here:

brainly.com/question/11374994

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