A cubical block of side 10 cm is surmounted by a hemisphere . What is the largest diameter that the hemisphere can have ?Find the cost of painting of total serface area of the solid so formed ,at the rate of rs 5 per 100sq cm (use value of 3.14)
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The largest diameter will be equal to the length of the cubicle block i.e. 10 cm otherwise it will not surmount the cube if it's diameter is greater than 10 cm it will be somewhat out of the boundary.
Area to be painted:
the side on which the hemisphere is surmounted will have 10x10 - 3.14 x 5 x 5
= 21.5 cm²
curved surface area of hemisphere= 2πr²
= 2 x 3.14 x 5 x 5
= 157 cm²
area of remaining sides of the cube= 10 x 10 x 5
= 500
Therefore area to be painted= 21.5 + 157 +500 = 678.5 cm²
Cost of painting= (678.5/100) x 5
= Rs. 33.925
Hope it helps..
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