Two similar spheres have a scale factor of 2:5. What is the ratio of their surface areas?

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Respuesta :

jsimpson11000 jsimpson11000 · Answer 1 · 2022-05-13T00:33:38+02:00

Answer:

4:25

Step-by-step explanation:

Sphere surface area = 4 pi r^2

now change r to 2.5 r ( to maintain the 2:5 ratio)

area2 = 4 pi (2.5 r)^2 = 6.25 * 4 pi r^2

so ratio of surface areas is 1 : 6.25 = 4:25

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jainveenamrata jainveenamrata · Answer 2 · 2022-05-31T08:40:00+02:00

If two similar spheres have a scale factor of 2:5. Then the ratio of their surface areas will be 4 / 25.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Two similar spheres have a scale factor of 2:5.

Let the r₁ and r₂ be the radius of the spheres. Then we have

r₁ / r₂ = 2 / 5

Then the surface area of the sphere is given as

Surface area = 4πr²

Then the ratio of their surface areas will be

[tex]\rightarrow \dfrac{4\pi r_1^2 }{4\pi r_2^2} = \left (\dfrac{r_1}{r_2} \right )^2[/tex]

Then we have

→ (2 / 5)²

→ 4 / 25

More about the geometry link is given below.

https://brainly.com/question/7558603

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