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The external and internal diameters of a hollow hemispherical vessel are 12cm and 10cm respectively. The cost of painting is Rs2 per sq. cm. Find the cost of painting the vessel all over.

the internal radius of the hemisphere be r=10/2=5 cm
the external radius of the hemisphere be R=12/2 = 6 cm
the surface area of the hemisphere = 2πr2+2πR2+π(R2-r2)
=π*[2*52+2*62+(62-52)]=227*[50+72+11]=227*133=22*19 =418 sq cm
the total cost of painting = 418*2= 836/-
hope this helps you.
 

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Inner radius of the hemisphere, r = 10/2 = 5 cm

Outer radius of the hemisphere, R = 12/2 = 6 cm

Area to be painted = Inner C.S.A. + Outer C.S.A. + Area of circular ring

= 2TTr2+ 2TTR2 + TT(R2 - r2)

= 2TTr2 + 2TTR2 + TTR2 - TTr2

= 3TTR2 + TTr2

= TT(3R2 + r2+

= 22/7{3(6)2 + (5)2}

= 22/7*133

= 418 cm2

Cost = Area to be painted * Rate

= 418*2

= Rs. 836

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