The radius of a conical tent is 7 meters and its height is 10 meters. Calculate the length of canvas used in making the tent if width of canvas is 2m.

The tent is in the shape of a cone.
The radius of the tent is given as 7 m and the height is given as 10 m as shown below.
The slant height l can be calculated from the formula l = \sqrt{r^{2}+h^{2}}
Substituting the values of r = 7 and h = 10 in the formula we get
l = \sqrt{49+100} = \sqrt{149} = 12.2 m
The surface area of the tent = \pi r l(since surface area of a cone is \pirl)
= \frac{22}{7}\times7\times 12.2 m^{2}
= 268.4m^{2}
Since the canvas covers the surface area of the tent, the area of the canvas is 268.4m^{2}
Length of the canvas = \frac{area}{width}
The width is given as 2m, and we have the area = 268.4m
So, the length of the canvas used = \frac{268.4}{2}=134.2 cm.
Step 1: Note down the given measurements
Radius of conical tent (r) = 7 meters
Height (h) = 10 meters.
Width of canvas = 2 meters
Step 2: Find the slant height of the cone
FORMULA: Slant height l^2 = r^2 + h^2
l = \sqrt{r^2 + h^2}
l = \sqrt{7^2 + 10^2}
l = \sqrt{49 + 100}
l = \sqrt{149} = 12.2 m
Step 3: Calculate the surface area of the conical tent
FORMULA: Surface area of the conical tent = \pi rl
= \frac{22}{7} * 7 * 12.2 m^2
= 268.4 m^2
Step 4: Determine the length of canvas used in making the tent.
Area of the tent = 268.4 m^2
Length * width = 268.4 m^2
Length = \frac{268.4}{width}
Length = \frac{268.4}{2}
Length = 134.2 m