Question

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

Answer 1

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

Answer 2

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

What is Geometry?

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

$\rightarrow \dfrac{4\pi r_1^2 }{4\pi r_2^2} = \left (\dfrac{r_1}{r_2} \right )^2$

Then we have

→ (2 / 5)²

→ 4 / 25

More about the geometry link is given below.

brainly.com/question/7558603

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