Question
The volumes of two hemispheres are in the ratio 1000:3375.
Determine the ratio of their total surface areas. (Take π = 22/7)Solution
ATQ,
Volume of a hemisphere = (2/3) × π × radius³
Let the radii of the two hemispheres be ‘A’ and ‘a’ unit’s respectively.
So,
[(2/3) × π × A³] : [(2/3) × π × a³] = 1000 : 3375
⇒ A³ : a³ = 1000 : 3375
⇒ A : a = 10 : 15 = 2 : 3
Total surface area of a hemisphere = 3 × π × radius²
So, required ratio = (3 × π × A²) : (3 × π × a²)
⇒ A² : a² = 2² : 3² = 4 : 9
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