Q. 14

# The outer and inner diameter of a hollow hemi–spherical vessel are 43 cm and 42 cm. Find the cost of colouring the vessel at 7 paise per square cm. The hemispherical bowl will look like as shown

To find the cost required to paint we first need to calculate its total surface area

Total surface area will include the area of outter curved surface the inner curved surface and the flat surface as shown

Diameter of outer surface = 43 cm

Radius of outer surface = ro = cm = 21.5 cm

Diameter of inner surface = 42 cm

Radius of inner surface = ri = cm = 21 cm

Curved surface area of hemisphere = 2πr2

outter curved surface area = 2πro2

= 2 × π × = π cm2

= 924.5π cm2

inner curved surface area = 2πri2

= 2 × π × 212

= 882π cm2

The flat area can be found by subtracting the inner circle area from outter circle area

flat area = πro2 – πri2

= π(21.5)2 – π(21)2

= 462.25π – 441π

= 21.25π cm2

Total surface area of hemispherical vessel = outter curved surface area + inner curved surface area + flat area

Total surface area of hemispherical vessel = 924.5π + 882π + 21.25π = 1827.75π cm2

Now cost of colouring 1 cm2 is 7 paise

So, cost of colouring 1827.75π cm2 = 7 × 1827.75 × π

= 7 × 1827.75 × = 1827.75 × 22

= 40210.5 paise

100 paise is 1 Rs

40210.5 paise = = 402.105 Rs

Therefore, cost of colouring the vessel is 402.105 Rs

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