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InterviewSolution
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The cost ofpainting the total surface area ofa cone at 25 paise per cm2 is?176. Fivolume of the cone, if its slant height is 25 cm. |
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Answer» Total cost = Rs. 176Rate of charge = 25 paise per sq.cm = Rs. 0.25 per sq.cm Total cost of painting cone = Total surface area of cone * Rate of charge=> Total surface area of cone = Total cost of painting cone / Rate of charge= 176/0.25= 704 sq.cm Let radius of cone be r cmslant height (l) = 25 cm Total surface area of cone = πr(r+l)=> 704 = πr(r+l)=> 704 = 22r(r+25)/7=> 704*7/22 = r^2+25r=> 224 = r^2+25r=> 0 = r^2+25r-224=> 0 = r^2+32r-7r-224=> 0 = r(r+32)-7(r+32)=> 0 = (r-7)(r+32)=> 0 = r-7 or 0 = r+32=> r = 7 or -32 Discarding negative value as radius cannot be negativeTherefore, radius of cone = 7 cm By Pythagoras Theorem, height of cone = (l^2-r^2)^1/2= (25^2-7^2)^1/2= (625-49)^1/2= (576)^1/2= 24 cm Therefore, volume of cone = πr^2h/3= 22*7*7*24/3*7= 1232 cm^3 |
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