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in Surface Areas And Volumes by (65.2k points)

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. Find the inner surface area of the vessel.

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(i) Diameter of a hollo hemisphere = 14 cm. 

∴ Radius of a hollow hemisphere, r 

r = 7 cm. 

Inner curved surface of a hemisphere = 2π2

= 14 × 22 = 308 sq. cm. 

(ii) Radius of hollow cylinder, r = 7 cm. 

Height, h = 13 – 7 = 6 cm. 

∴ Inner Surface area of the Cylinder, 

= 2πrh

= 2 x \(\frac{22}{7}\) x 7 x 6

= 44 × 6 = 264 sq.cm. 

∴ Inner surface area of the vessel = Area of hemisphere + Area of cylinder 

= 308 + 264 

= 572 sq. cm.

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