Question

the cost of painting the curved surface area of a cone a 5 paise per is rs 35.20.Find the volume of the cone if it's slant height is 25cm​

Answer 1

       Volume if the cone is 1232 cubic cm.

• Total cost = Rs. 35.20
• Rate of charge = 5 paise per sq.cm = Rs. 0.05 per sq.cm  
• Total cost of painting cone = Total surface area of cone * Rate of charge
• So, Total surface area of cone = Total cost of painting cone / Rate of charge= 35.20/0.05= 704 sq.cm
• Let’s assume radius of cone be r cm
• Slant height (l) = 25 cm
• Total surface area of cone = πr(r+l)
• So, 704 = πr(r+l)
• So, 704 = 22r(r+25)/7
• So,  704*7/22 = r^2+25r
• So,  224 = r^2+25r
• So,  0 = r^2+25r-224
• So,  0 = r^2+32r-7r-224
• So,  0 = r(r+32)-7(r+32)
• So,  0 = (r-7)(r+32)
• So,  0 = r-7 or 0 = r+32
• So,  r = 7 or -32
• Negative value can’t be radius.  
• So, 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 cubic cm