104
'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'.
Show SolutionHide Solution↓
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)