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'Gilli Danda' is a very popular traditional game of India which is played with two wooden sticks - the larger one is called 'Danda' and smaller one 'Gilli'.
'Danda' - It is cylindrical in shape with diameter $4$ cm and length $42$ cm.
'Gilli' - It is cylindrical in middle with identical conical ends of same radius $1.5$ cm and length $2.8$ cm. The length of cylindrical part is $7$ cm.
Based on the above, answer the following questions :
(i) Find the volume of wood used in making both the conical parts of Gilli.
(ii) Find the volume of wood used in making 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
(b) Find the total surface area of 'Danda'.
'Danda' - It is cylindrical in shape with diameter $4$ cm and length $42$ cm.
'Gilli' - It is cylindrical in middle with identical conical ends of same radius $1.5$ cm and length $2.8$ cm. The length of cylindrical part is $7$ cm.
Based on the above, answer the following questions :
(i) Find the volume of wood used in making both the conical parts of Gilli.
(ii) Find the volume of wood used in making 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
(b) Find the total surface area of 'Danda'.
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Solution: (i) Required Volume = $2 \times \frac{1}{3} \times \frac{22}{7} \times 1.5 \times 1.5 \times 2.8$ (1/2 Mark)
= $13.2$ cm$^3$ (1/2 Mark)
(ii) Required Volume = $\frac{22}{7} \times 1.5 \times 1.5 \times 7$ (1/2 Mark)
= $49.5$ cm$^3$ (1/2 Mark)
(iii) (a)Volume of cylindrical log = $\frac{22}{7} \times 1.5 \times 1.5 \times 14 = 99$ cm$^3$ (1 Mark)
Volume of gilli = $13.2 + 49.5 = 62.7$ cm$^3$ (1/2 Mark)
Volume of wood scrapped = $99 - 62.7 = 36.3$ cm$^3$ (1/2 Mark)
OR
(b) TSA of Danda = $2 \times \frac{22}{7} \times 2 \times 2 + 2 \times \frac{22}{7} \times 2 \times 42$ (1 Mark)
= $\frac{3872}{7}$ cm$^2$ or $553.14$ cm$^2$ (1 Mark)
= $13.2$ cm$^3$ (1/2 Mark)
(ii) Required Volume = $\frac{22}{7} \times 1.5 \times 1.5 \times 7$ (1/2 Mark)
= $49.5$ cm$^3$ (1/2 Mark)
(iii) (a)Volume of cylindrical log = $\frac{22}{7} \times 1.5 \times 1.5 \times 14 = 99$ cm$^3$ (1 Mark)
Volume of gilli = $13.2 + 49.5 = 62.7$ cm$^3$ (1/2 Mark)
Volume of wood scrapped = $99 - 62.7 = 36.3$ cm$^3$ (1/2 Mark)
OR
(b) TSA of Danda = $2 \times \frac{22}{7} \times 2 \times 2 + 2 \times \frac{22}{7} \times 2 \times 42$ (1 Mark)
= $\frac{3872}{7}$ cm$^2$ or $553.14$ cm$^2$ (1 Mark)