# The cost of painting the total surface area of a cone at 25 paise per cm^2 is Rs. 176. Find the volume of the cone, if its slant height is 25 cm.

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by Ali548

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by Ali548

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Rate 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 cm

slant 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 negative

Therefore, 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 cu. cm