Question

the ratio of the volumes of 2 spheres is 1:8. Find the ratio of their surface areas​

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

1:4

Explanation:

Volume of sphere = 4/3πr³

Let radius of first sphere be r₁

Let radius of second sphere be r₂

→4/3πr₁³ : 4/3πr₂³ = 1 : 8

→r₁³ : r₂³ = 1 : 8

→r₁³/r₂³ = 1/8

→(r₁/r₂)³ = (1/2)³

→r₁/r₂ = 1/2

→r₁ : r₂ = 1 : 2     ⇒ (i)

Surface area of sphere = 3πr²

Let surface area of first sphere = 3πr₁²

Let surface area of second sphere = 3πr₂²

→3πr₁² : 3πr₂²

→r₁² : r₂²

→(r₁ : r₂)²

After putting the value of (r₁ : r₂) from (i), we get :-

(1 : 2)²

→1 : 4

Hence, the ratio of the given spheres' surface areas would be 1 : 4