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ICSE / ISC eBooks

Example – 13. Find the volume, curved surface area and total surface area of a hemisphere whose diameter is 14 cm. (Use π = 22/7).

Solution :-  Volume of a hemisphere = (2/3)πr³ = (2/3)(22/7)(14/2)³

= (2/3)(22/7)(7)(7)(7)

= 2156/3 = 718.66 cm³.

Curved surface area = 2πr²  = (2)(22/7)(7)² = 308 cm².

Total surface area = 3πr²  = (3)(22/7)(7)² = 462 cm².

Example – 14.  The internal and external diameter of a hollow hemispherical vessel are 14 cm and 21 cm respectively. The cost of silver plating of 1 cm² of  the surface is Re. 0.40. Find the total cost of silver plating the vessel all over. (Use π = 3.14).

Solution :- Let external and internal radii be R and r respectively

 Total surface area to be painted = External curved surface area of hemisphere + Internal curved surface area of hemisphere + Area of the edge

= 2πR² + 2πr² + π(R³ – r²)

= 3πR² + πr²

= π(3R² + r²)

= 3.14 × {3 × (21/2)² + (7)²}

= 1192.415 cm²

Cost of painting = Rs. 0.40 × 1192.415
                         = Rs. 476.97.