What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use π = 3.14)
Solution:
Since the tent is in a conical shape, the area of tarpaulin = the curved surface area of the cone.
The curved surface area of a right circular cone with base radius(r) and slant height(l) is πrl
where, Slant height, l = √(r2 + h2), h is the height of the cone.
The length of the tarpaulin can be calculated by dividing its area by its breadth.
Since the extra length of material = 20 cm, the actual length of the tarpaulin will be obtained by adding 20 cm to the length of the tarpaulin.
Radius, r = 6 m
Height, h = 8 m
Slant height, l = √r² + h²
= √(6)² + (8)²
= √36 + 64
= √100
= 10 m
Therefore, the curved surface area = πrl
= 3.14 × 6m × 10m
= 188.4 m2
Now, width of the tarpaulin = 3m
Area of the tarpaulin = 188.4 m2
So, Area of the tarpaulin = width of the tarpaulin × length of the tarpaulin
188.4 m2 = 3 × length of the tarpaulin
⇒ Length of the tarpaulin = 188.4 m2/3
= 62.8 m
Extra length of the material = 20cm = 20/100m = 0.2m
Actual length required = 62.8m + 0.2m = 63m
Thus, the required length of the tarpaulin is 63 m.
☛ Check: NCERT Solutions for Class 9 Maths Chapter 13
Video Solution:
What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use π = 3.14)
Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.3 Question 5
Summary:
It is given that there is a tarpaulin of 3 m width will be required to make a conical tent of height 8 m and base radius 6 m. Assuming that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm, we have found that the required length of the tarpaulin is 63 m.
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