Final answer:
To find the length of canvas used for the tent, we calculate the radius of the base using the circumference, find the slant height using the Pythagorean theorem, and then calculate the surface area of the conical part. Finally, we divide the area by the width of the canvas to get the required length of canvas, which is 190.2 meters.
Step-by-step explanation:
To find the length of canvas needed to make the tent, we first need to calculate the radius of the base of the conical tent. Since the circumference (C) is given as 44 meters and we know C = 2πr, we can solve for r as follows:
r = C / (2π)
= 44 / (2 × (22/7))
= 7 meters
Next, using the Pythagorean theorem on the right-angled triangle formed by the height (h), the radius (r), and the slant height (l) of the cone, we find the slant height (l):
l = √(h² + r²)
= √(10² + 7²)
= √(100 + 49)
= √149
≈ 12.2 meters
The surface area (A) of the conical part is given by
A = πrl
= (22/7) × 7 × 12.2 =
380.4 square meters
Finally, since the width of the canvas is 2 meters, the length of canvas required would be
A / width = 380.4 / 2
= 190.2 meters.