44. The internal and external diameters of a hollow hemispherical vessel are
10 cm and 11 cm respectively. If the cost of painting 1 cm² of the surface
area is 0.05, find the total cost of painting the vessel all over.
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Internal diameter of spherical vessel =24 cm
External diameter of hemispherical vessel =25 cm
Internal radius =r=12 cm and External radius =R=12.5 cm
Total surface area to be painted
= External curved surface + Internal curved surface + Area of ring
=2πR2+2πr2+π(R2−r2)
=π(2R2+2r2+R2−r2)
=π(3R2+r2)
=722(3×12.52+122)
=722(468.75+144)
=722×612.75
=1925.78sq.cm
Rate of painting =5paise per sq.cm
Thus, cost of painting=Area×Rate=1001925.78×5=Rs.
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