ART INTEGRATED LEARNING MATHEMATICS (Sikkim) Project work to be done by group of 5 students. ROLL NO. PROJECT ROLL NO. PROJECT 1 - 5 1 21 - 25 1 6 - 10 2 26 - 30 2 11 - 15 3 31 - 35 3 16 - 20 4 36 - 40 4 41 - 45 5 All work to be done on A-4 sheets/slides. Cover page/slide should mention topic of the project. Photographs/sketches should be well labeled. Names, class and section of students of the group to be mentioned on last page/ slide. 1 TRADITIONAL HOUSE DESIGN a) Collect information about traditional houses of different ethnic communities of Sikkim and different combination of solid shapes used. Special features of these houses(paste photographs/ ppt) b) Draw a Sikkimese house from one point perspective as learnt in art class. C) A Lepcha traditional house The Lepcha people are aboriginal inhabitants of Sikkim. The construction of this house displays the ingenuity of an age old tradition of laying the super structure on open surface (over stone slabs) to counter the effects of powerful earthquakes. To construct his house a Lepcha (a Sikkimese aboriginal) uses logs of wood for 8 stilts. i) Stilts are cylindrical at base of diameter 70cm. Up to height of 1.2m mounted by cuboidal pieces 50cm x 50cm x 75 cm. How many cubic meters of wood will be required to construct the stilts. ii) To reach the house , he uses 13 steps each 1m long,40cm wide and 15cm high. Calculate the total volume of concrete required to build the stairs. iii) How many stone slabs 90cm by 60cm are required to construct floor 12m by 9m. iv) Find the cost of painting the wooden walls at rate of 70paise per sq. m if the house is 8mx5mx3m. (Refer photograph). 2 GEOMETRY IN ARCHITECTURE SIKKIM is home to many monasteries with stunning architecture and colorful interiors. Collect information about architecture, decoration on the walls and salient features of these buildings with reference to plane and solid geometry. ( Any 5 monastries, text should be supplemented with lots of images and graphics.) 3 GEOMETRY IN FLAGS The Kingdom of Sikkim had used several flags during its history. With the admission of Sikkim to the Republic of India and with the abolition of the monarchy, the flag lost its official status in 1975. a) Collect information about different flags used by kingdom of Sikkim before 1975 and different combinations of plane figures used. (paste photographs/ ppt) b) Draw the above flag (1967-1975) using geometrical instruments and colour it. c) A child tries to draw the flag with inner white circle of radius2.0 cm and inner gold band of width 1cm. The outer white band (ring) of width 3cm is divided into 8 equal regions by golden strokes and an outer gold band of width 2cm. i) Calculate the area of inner white circle. ii) Find the area of inner gold band of width 1cm. iii) Calculate the area of each of 8 white regions included between golden strokes (Assume that each golden stroke has negligible thickness) iv) Find the area of outer gold band of width 2cm. v) The child tries to decorate the border by using red satin ribbon. What is the length of ribbon required if flag is 15cm long and12 cm wide.(Give your answer in ) 4 MATHEMATICS IN PRAYER WHEEL Buddhism is dominant religion in Sikkim. Sikkimese Buddhist worshippers turn prayer wheels to accumulate merit, to help all beings in the world and to purify their karma. A prayer wheel is cylindrical wheel (khorlo) on a spindle made from metal, wood, stone, leather or coarse cotton. The cylinder itself is affixed with a cord or chain terminating in a metal weight allowing it to be spun by a slight rotation of the wrist. a) Make a model of the prayer wheel using colored sheet and decorate the cylindrical part. -------------------19cm---------------------- 7cm ------6.3cm------- -----6.3cm------ ---2.8cm--- 1. Cut pieces from any decorative or colored sheet as shown above. Roll the rectangle and paste to form the hollow cylinder of height 7cm. 2. Paste two circles of diameter 6.3cm on two ends of cylinder to make a closed cylinder. 3. Paste circle of diameter 2.8cm of different colour on top. 4. Paste hemisphere/sphere at centre point of top circle and paste cone (fold sector and paste along edge) on top of hemisphere/sphere. 5. Make a cylinder of length 10cm and diameter 2cm by rolling newspaper and fix below the main cylinder as handle. c) An artisan makes the prayer wheel from metal sheet. Hollow Cylindrical part of diameter 6cm and height 7cm is covered by two circular metal plates of diameter 6.3cm at base and top. Spindle on which the cylinder rotates is covered on top by a circular plate of diameter 2.8cm which is mounted by an open hemisphere of diameter 2.8cm and cone of same radius and height 2.1cm. Base of spindle is covered by a cylindrical wooden handle of radius 1cm and length 10cm. A small metallic ball of radius 6mm is attached by a chain. i) Find the area of metal sheet required to make the wheel ii) Calculate the volume of wood required to construct the handle. iii) Find the volume of metallic ball of 6mm attached to the cylinder by chain. 5 HEIGHTS AND DISTANCES The natural attractions like panoramic mountain viewpoint, mountainous ranges, valleys, waterfalls, natural lakes, vegetations, ethnic villages etc., are the places of special interest for the visitors to Sikkim. a) Sketch snow covered peaks of kanchenjunga. b) A tourist visiting Sikkim (Pelling village) observes mountain peaks. Determine the height of the mountain if the angle of elevation of its top at an unknown distance is 60. At a distance 10 km further away from mountain, along the same line, the angle of elevation becomes 30 . .