Question

what length of a canvas 4 m wide is required to make a conical tent 4 m radius and 5.6 m height. find the cost of canvas at the rate of Rs 96 per m

Answer 1

Answer:

Rs 168.96

Step-by-step explanation:

Given ,

radius of the conical tent 'r' = 4 m

(Assuming the given height as slant height of the conical tent)

slant height of the conical tent 'l' = 5.6 m

Let the length of the canvas be 'l'

Given width of the canvas 'w' = 4 m

But l*w = π*r*l Curved Surface Area of the conical tent

Thus, l*4 = π*4*5.6 = 7.04 (If we consider π as 22/7)

=> l = 1.76 m

Thus, length of the canvas = 1.76 m.

Given cost of the canvas = Rs 96 per m

Hence, Cost of the canvas for length of 1.76 m will be

=1.76 *96

=168.96 Rs

Answer 2

Answer:

Length of canvas used =21.63 m

total cost of canvas = 2076.36 Rs

Solution:

To find the length of the canvas:

First calculate the Curved Surface Area of cone,since Tent is open from bottom,so we need not to take Total Surface area.

CSA of Cone =
$\pi \times r \times l \\ \\ r = 4 \: m \\ \\ h = 5.6 \: m \\ \\ {l}^{2} = {4}^{2} + {(5.6)}^{2} \\ \\ {l}^{2} = 16 + 31.36 \\ \\ = 47.36 \\ \\ l = 6.88 \: m \\ \\ C.S.A. = \frac{22}{7} \times 4 \times 6.88 \\ \\ = 86.51 \: {m}^{2}$

Since width of canvas is given as b= 4 m

let length is l

$l \times b = 86.51 \\ \\ l = \frac{86.51}{4} \\ \\ l = 21.63 \: m$

Since canvas is of length 21.63 m and cost of 1 meter is 96 rupees

So,total cost of canvas is

$= 21.63 \times 96 \\ \\ = 2076.36 \: Rs$