Question

The cost of painting the total surface area of a cone at 25 paise per cm² is ₹176. Find the volume of the cone, if its slant height is 25 cm.

Answer 1

Slant height of the cone, l = 25 cm 

Total cost at the rate of 25 p/cm²

= ₹176 

∴ Total surface area of the cone

= 176/25 x 100 = 176 x 4 = 704cm²

But T.S.A. of the cone = πr (r + l) = 704 

Thus 22/7 r(r + 25) = 704

r(r + 25) = \(\frac {704\times7}{22}\) = 224

r² + 25r = 224 

⇒ r² + 32r – 7r – 224 = 0 

⇒ r (r + 32) – 7 (r + 32) = 0 

⇒ (r + 32) (r – 7) = 0 

⇒ r = 7 (∵ ’r’ can’t be negative)

∴ Volume of the cone = 1/3 πr²h

= 1/3 x 22/7 x 7 x 7 24

= 22 x 7 x 8 = 1232cm³