The ratio between the volumes of two spheres is 8:27. What is the ratio between the surface areas?
Given: Volumes of the spheres are in the ratio 8:27.
Volume of a sphere is given by: πr3 (here ‘r’ is the radius of the sphere).
Surface are of a sphere is given by: 4πr2 (here ‘r’ is the radius of the sphere).
Let r1, r2 be the radii of first sphere and second sphere respectively.
∴ π(r1)3: π(r2)3 = 2:27
⇒ (r1)3: (r2)3 = 8 : 27
⇒ r1: r2 = ∛8 : ∛27
⇒ (r1): (r2) = 2: 3
Now , here
4π(r1)2: 4π(r2)2 = (r1)2 : (r1)2
⇒ (r1)2 : (r1)2 = (2)2 : (3)2 = 4:9
∴ Ratio of the surface areas of the given spheres is 4:9.
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