A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. What is the inner surface area of the vessel?

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  1. 172 cm2
  2. 572 cm2
  3. 372 cm2
  4. 772 cm2

Answer (Detailed Solution Below)

Option 2 : 572 cm2
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Detailed Solution

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Concept:

CSA of cylinder = 2πrh

CSA of hemisphere = 2πr2

Calculation:

61910aa252d184bb7a484783 16382124031731

Since the diameter is the same for both the cylinder as well as the hemisphere.

∴ Radius, r = 14/2 = 7 cm

Height of the cylinder, h = 13 - 7 = 6 cm

So, the surface area of the vessel = CSA of the cylinder (as the cylinder is hollow) + CSA pf hemisphere 

⇒ 2πrh + 2πr2 

⇒ 2πr(h + r)

\(⇒ 2× \frac{22}{7}× 7(6+7)\)

⇒ 44 × 13 = 572 cm2

Hence, the surface area of the vessel is 572 cm2.

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