Question

A Piece of canvas having area 552 m2 is being used to make a conical tent with a base (5) radius of 7 m. Assuming that all the stitching margins and wastage incurred while cutting approx to 2 m2, find the volume of the tent that can be made with the given piece of canvas​

Answer 1

Answer:

usable area for tent = 552 - 2 = 550 m^2

area of cone =

$\pi \: rl = \frac{22}{7} \times 7 \times l$

$550= \frac{22}{7} \times 7 \times l \\ l = \frac{550}{22} = \frac{50}{2} = 25 \: m$

height of tent,

$l = \sqrt{ { h}^{2} + {r}^{2} } \\ 25 = \sqrt{ {h}^{2} + {7}^{2} } \\ 625 = {h}^{2} + 49 \\ {h}^{2} = 576 \\ h = 24$

now, volume of tent

$v = \frac{1}{3} \times \pi \times {r}^{2}h \\ = \frac{1}{3} \times 49 \times 24 = 392 {m}^{3}$