Question

Monica has a piece of canvas whose area is 551 m^2 . She uses it to make a conical tent made, with a base radius of 7 m. Assuming that all the stitching and the wastage incurred while cutting, amounts to approx 1 m^2. Find the volume of the tent?

Answer 1

Step-by-step explanation:

To prove :

Find the volume of the tent .

solution :

[ Take π = 22/7 ]

radius (r) = 7 cm

Curved surface area of the conical tent = Area of the of the canvas - area of the wastage used

= 551 m² - 1 m²

= 550 m²

=> πrl = 550 m²

\boxed { Curved \: surface \: Area \: = πrl }

\implies \frac{22}{7}\times 7\times l = 550

=> l = ( 550 )/22

=> l = 25 m

\boxed { h^{2} = l^{2}-r^{2} }

=> h² = 25² - 7²

=> h² = 625 - 49

=> h² = 576

=> h = √576

=> h = √24²

=> h = 24 m

Now ,

\boxed { Volume \: of \: a : cone = \frac{1}{3}\times π\times r^{2}\times h}

V = (1/3) × (22/7) × 7² × 24

= (22×7×7×24)/(3×7)

= 22×7×8

= 1232 m³

Therefore,

Volume of the conical tent (V) = 1232 m³