Q9 of 24 Page 227

The quantity of iron sheet to make boya of right circular conical shape is m2. If the slant height of it is 5m, then let us write, by calculating, the volume of air in the boya and its height. Let us determine the expenditure to colour the whole surface of the boya at the rate of ₹2.80 per m2. [The width of the iron-sheet not to be considered while calculating.]

Let, base radius = r m


Slant height, l = 5 m


According to problem,




⇒ r2 + 5r = 24


⇒ r2 + 8r – 3r – 24 = 0


⇒r(r + 8) – 3(r + 8) = 0


⇒ (r + 8)(r – 3) = 0


⇒ r = -8 or 3


∴ base radius = 3 m


∴ height of the boya, h = √(52 – 32)


= √(25 – 9) = 4 m


∴ volume of air in the boya,


= πr2h/3


= 22/7 × 32 × 4/3


⇒ 37.71 m3


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