The vertical height of a right circular conical tent is 4m and the volume of space inside it is 968/7 cubic metre. Find the canvas required to make the tent.

Respuesta :

the equation for the volume of a conical tent is 
v = 1/3 * height * area of the base
   = 1/3 ×hπr²
where v - volume 
h - height of the conical tent 
r - radius of base circle 
area of the base = 3v/h
                 πr²     = 3 *968/7 m³ /4 m
                   r²     = 3 * 968 * 7 / (7 * 22* 4 )
                           = 33
                   r = 5.74 m 
area of the curved surface = πrl
where l is the slant height 
l² = r² + h² 
   = 5.74² + 4²
    = 33 + 16
    = 49 m
l = 7 m
then the area of the curved surface is ;
area = πrl
        = (22/7) * 5.74 * 7 
        = 126.28 m²
the canvas should have area 126.28 m² to cover the tent