Q. 305.0( 4 Votes )
The volumes of two Spheres are in the ratio 64: 27. The ratio of their surface areas is
Given: Volume ratio of two Spheres is: 64:27
Volume of the Sphere is: × π × r3 (where r is radius of sphere)
Surface area of the sphere is: 4 × π × r2 (where r is radius of sphere)
Let S1 and S2 be two different spheres.
(Volume of) S1: (Volume of) S2 = 64:27
× π × (r1)3: × π × (r2)3 = 64:27 (here r1 and r2 are the radii of S1 and S2 respectively)
(r1)3: (r2)3 = 64:27
r1: r2 = ∛64:∛27
r1: r2 = 4:3
Let SA1 and SA2 be the surface areas of the spheres S1 and S2 respectively.
∴ SA1:SA2 = 4 × π × (r1)2:4 × π × (r2)2 (here r1 and r2 are the radii of S1 and S2 respectively)
⇒ SA1:SA2 = (r1)2: (r2)2
⇒ SA1:SA2 = (4)2: (3)2
⇒ SA1:SA2 = 16:9
∴ The ratio of the Surface area of spheres is: 16:9
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