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The ratio of the lengths of the radii of two spheres is 5 : 8. What is the ratio of the surface area of the smaller sphere to the surface area of the larger sphere?

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Answer:

The ratio of the surface area of the smaller sphere to the surface area of the larger sphere is 25:64.

Explanation:

The surface area of square is given by formula as follows :


A=4\pi r^2

r is radius of sphere

The ratio of the lengths of the radii of two spheres is 5 : 8. The ratio of the surface area of the smaller sphere to the surface area of the larger sphere is :


(A_1)/(A_2)=(r_1^2)/(r_2^2)

Here,
(r_1)/(r_2)=(5)/(8)


(A_1)/(A_2)=(25)/(64)

So, the ratio of the surface area of the smaller sphere to the surface area of the larger sphere is 25:64.

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