Question

Kumbh Mela is a major pilgrimage and festival in Hinduism. It is celebrated in a cycle of

approximately 12 years at four river-bank pilgrimage sites: the Prayagraj (Ganges-Yamuna

Sarasvati rivers confluence), Haridwar (Ganges), Nashik (Godavari), and Ujjain (Shipra).

Government of UP is planning to procure tent for the pilgrims

during Kumbh Mela.The specification of tent is given below.

(i) Top conical part must have a white colored thick fabric whose cost is Rs.60 per square

meter.

(ii) Lower cylindrical part must have PVC coated blue fabric whose cost is Rs. 70 per square

meter.

The front view section of tent is given below with dimension

(i) How much white fabric is required?

(a) 2640 sq. meter (b) 1914 sq. meter (c) 1320 sq. meter (d) 3828 sq. meter

(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

(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

(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 1

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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