How many metres of cloth, 5 m wide will be required to make a conical tent, the radius of whose base is 7 m and height is 24 m?

Assuming that there is no wastage in cloth and no extra cloth is required at the seams the total area of cloth used will be equal to the lateral surface area (L) of the conical shaped tent. This is given by the formula:

L = (pi)*r*S

Where:

r = radius of the base of the tent = 7 m (given)

S = slant height

the slant height is given by the formula:

S = (r^2 + h^2)^(1/2)

where: h = height of tent = 24 m (given)

Therefore:

S = (7^2 +24^2)^(1/2) = (49 + 576)^(1/2) = 625^(1/2) = 25

Substituting the values of S and r in equation for slant area we get.

L = (22/7)*7*25 = 550 m^2

let

l = length of the cloth required to make the conical tent.

w = width of the cloth = 5 m given

Then:

L = w*l = 5*l

But as we have calculated above L = 550 m^2

Therefor: 550 = 5*l

Therefor: l = 550/5 = 110 m

Answer:

Length of cloth required = 110 m