'Gilli Danda' is a popular traditional game of India played with tw...

Question

'Gilli Danda' is a popular traditional game of India played with two wooden sticks - the larger one 'Danda' and smaller one 'Gilli'. 'Danda' is cylindrical with diameter 4 cm and length 42 cm. 'Gilli' is cylindrical in the middle with identical conical ends of radius 1.5 cm and length 2.8 cm; the length of the cylindrical part is 7 cm.
(i) Find the volume of wood used in making both the conical parts of Gilli.
(ii) Find the volume of wood used in making the cylindrical part of Gilli.
(iii)(a) A cylindrical log of wood of radius 1.5 cm and length 14 cm is used to make Gilli. Find the volume of the wood scrapped.
OR
(iii)(b) Find the total surface area of 'Danda'.

Accepted Answer

Gilli: cone radius $r=1.5$ cm, cone height $h=2.8$ cm (two cones); cylindrical part radius $1.5$ cm, height $7$ cm.

(i) $$V(	ext{2 cones})=2	imes\frac13\pi r^2h=2	imes\frac13	imes\frac{22}{7}	imes2.25	imes2.8=2	imes6.6=13.2\ cm^3$$

(ii) $$V(	ext{cylinder part})=\pi r^2h=\frac{22}{7}	imes2.25	imes7=22	imes2.25=49.5\ cm^3$$

(iii)(a) Volume of Gilli (cylinder+2cones) $=13.2+49.5=62.7\ cm^3$. Volume of log (radius 1.5 cm, length 14 cm): $$V(	ext{log})=\pi r^2h=\frac{22}{7}	imes2.25	imes14=99\ cm^3$$ Volume of wood scrapped $=99-62.7=36.3\ cm^3$

OR

(iii)(b) Danda: radius $=2$ cm, length $=42$ cm. $$TSA=2\pi r(r+h)=2	imes\frac{22}{7}	imes2	imes(2+42)=2	imes\frac{22}{7}	imes2	imes44\approx553.14\ cm^2$$

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