Question

The cost of painting the total surface area of a cone at 25paisa persq is Rs 176 .find the volume of the cone if it's slant height is 25cm

Answer 1

Total cost = Rs. 176
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

Answer 2

the answer is 1232 cu.cm