Multiple choice

The curved surface of a hemisphere whose internal & external radii are a & b respectively, will be -

  1. $\displaystyle \pi \left( { a }^{ 2 }+{ b }^{ 2 } \right) $
  2. $\displaystyle 2\pi \left( { a }^{ 2 }+{ b }^{ 2 } \right) $
  3. $\displaystyle 2\pi \left( { a }^{ 2 }-{ b }^{ 2 } \right) $
  4. $\displaystyle 2\pi \left( { b }^{ 2 }+{ a }^{ 2 } \right) $
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B Correct answer
AI explanation

A hollow hemisphere has both an outer and an inner curved surface. The outer curved surface area is $2\pi b^2$ and the inner curved surface area is $2\pi a^2$. The total curved surface area is the sum of these two areas, which is $2\pi b^2 + 2\pi a^2$. Factoring out the $2\pi$ gives $2\pi (b^2 + a^2)$. The total curved surface area is $2\pi(a^2 + b^2)$.

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