Question

A circus tent is in the shape of cylindrical surmounted by a cone the diameter of the cylindrical portion is 24 m and its height is 11 meet the vertex of the cone is 16 m above the ground find the area of the canvas used to make the tent

Answer 1

Given diameter of a cylindrical portion
of the tent (d) = 24 m

radius (r ) = d /2 = 24 /2 = 12 m

height of cylindrical portion

h = 11 m

step 1 Find curved surface area (CSA) of cylindrical portion :
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C.S.A of cylinder = 2πrh

= 2π × 12 × 11

= 264 π m^2

step 2 Find slant height(l) and curved surface area(CSA) of cone :
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height of cone(h) = vertex - height of cylinderical
portion = 16 - 11 = 5 m

radius of cone(r) = radius of cylinderical portion(r) =12 m

slant height of cone :
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l = √( r^2 + h^2 )

= √[ (12)^2 + (5)^2 ]

=√169 = 13 m

slant height (l ) = 13 m

step3 Find CSA of cone :
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curved surface area of cone = πrl

= π × 12 × 13 m^2

= 156 m^2

step 4 Find the area of canvas used :
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Area of the canvas used

= CSA of cylinderical portion + CSA of cone

= 264 m^2 + 156 m^2 ,

= 420 π m^2

= 420 × 22 / 7

= 1320 m^2

therefore , area of the canvas used to make the tent = 1320 m^2
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Your Answer : required area = 1320 m^2
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