1. CASE STUDY:4 MARKS
Kumbh Mela is a major pilgrimage and festival in Hinduism. The pilgrims believe that bathing in the rivers
will cleanse them of their sins. Government is planning to procure tents for the pilgrims during Kumbh Mela.
The specification of each tent is given below:
a) Lower cylindrical part must have a thick red and blue fabric whose cost is rupees 60 per sq.m.
b) The top conical part must have PVC coated red fabric whose cost is rupees 70 per sq.m.
29 in
20 m
5 m
42 mn
Different view section of the tent is given below with dimensions.
Answer any four questions:
1) How much thick red and blue fabric is required.
2) How much PVC coated red fabric is required.
3) :f labour charge for the construction of tent is rupees 150, what is the total cost of one tent.
4) What is the total floor area of one tent.
5) If the floor area required by one pilgrim 6 sq.m how many pilgrims can be accommodated in one
tent.
Answers
what type of question is this ??
Question (i) :- How much white fabric is required ?
(a) 2640 sq. meter (b) 1914 sq. meter (c) 1320 sq. meter (d) 3828 sq. meter .
Answer :-
As it is given that, Top conical part must have a white colored fabric.
from image we have,
Radius of cone = 42/2 = 21 cm.
Slant height = 29 cm .
so,
→ surface area of conical tent = π * radius * slant height = (22/7) * 21 * 29 = 1914 m² (b) (Ans.)
Question (ii) :-How much blue PVC coated fabric is required ?
(a) 1320 sq. meter (b) 330 sq. meter (c) 660 sq. meter (d) 240 sq. meter
Answer :-
As it is given that, Lower cylindrical part must have PVC coated blue fabric .
from image we have,
Radius of cylinder = 42/2 = 21 cm.
Height = 5 cm .
so,
→ surface area of cylindrical tent = 2 * π * radius * height = 2 * (22/7) * 21 * 5 = 660 m² (c) (Ans.)
Question (iii) :- If labour charge for the construction of tent is Rs.15 per sq. meter what is the total cost of tent ?
(a) Rs. 243100 (b) Rs. 129800 (c) Rs. 199650 (d) Rs. 243800
Answer :-
given that,
Labour charge = Rs.15 / m².
White coloured charge = Rs.60 / m².
Blue coloured charge = Rs.70 / m².
so,
→ Total cost = conical area * (White coloured charge + Labour charge) + cylindrical area * ( Blue coloured charge + Labour charge)
→ Total cost = 1914(60 + 15) + 660(70 + 15)
→ Total cost = 1914 * 75 + 660 * 85
→ Total cost = 143550 + 56100
→ Total cost = Rs.199650 (c) (Ans.)
Question (iv) :- If space requirement of a pilgrims is 6 sq. meter, how many pilgrims can be accommodated in a tent ?
(a) 142 (b) 231 (c) 196 (d) 346
Answer :-
→ Total floor area of tent = π * (radius)² = (22/7) * 21 * 21 = 1386 m².
then,
→ Total number of pilgrims can be accommodated in a tent = Total floor area of tent / space requirement of a pilgrims = 1386 / 6 = 231 Pilgrims (b) (Ans.)
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