Pragya donates toys to children of a nominee to the occasion of her birthday is toy is in shape of a cone mounted on a hemisphere of common base radius 7 centimetre the total height of the toy is 31 CM find the total surface area of the toy Also find the cost of 50 such toys if the cost of material used for colouring the toy is 5 per 100 cm and cost of manufacturing is 10 rs per day

Given  :   A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm.The total height of the toy is 31 cm. We form that toy , As :
 
Here

Height of cone  =  31  - 7   =  24 cm
And
Radius of cone  =  radius of hemisphere  =  7 cm
And
Total surface area of toy  =  Curved surface area of cone  +  Curved surface area of hemisphere

And
 

we know Curved surface area of cone  = πrl  , Where l = h2 +  r2−−−−−−−√ 
So,
Curved surface area of cone = 227× 7 ×  242 + 72−−−−−−−√ =  22 × 576 + 49−−−−−−−√ = 22 × 576 + 49−−−−−−−√ =  22 × 625−−−√ =  22 × 25 =  550  cm2 
And
Curved surface area of hemisphere = 2πr2 
 = 2×227× 7 × 7  =  44 × 7 =308  cm2 
Then
Total surface area of toy  =  550 + 308  = 858 cm²                                    ( Ans ) 

And
Total surface area of 50 toys  =  50 × 858  = 42900   cm² 
And
Cost of material used in the toys 5 rupees per 100 cm² 
So,
Cost of material used in the toys  =  5 × 429  = Rs. 2145
And
Cost of making is rupees 10 per toy.
So,
Cost of making 50 toys  =  50 × 10  =  500
So,

Total cost of 50 toys  =  2145 +  500 =  Rs. 2645    


Regards