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Question -

A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of canvas required for the tent.



Answer -


Given,

The diameter of thecylinder (also the same for cone) = 24 m.

So, its radius (R)= 24/2 = 12 m

The height of theCylindrical part (H1) = 11m

So, Height of the conepart (H2) = 16 – 11 = 5 m

Now,

Vertex of the coneabove the ground = 11 + 5 = 16 m

Curved Surface area ofthe Cone (S1) = πRL = 22/7 × 12 × L

The slant height (L)is given by,

L = √(R2 +H22) = √(122 + 52) = √169

L = 13 m

So,

Curved Surface Area ofCone (S1) = 22/7 × 12 × 13

And,

Curved Surface Area ofCylinder (S2) = 2πRH1

S=2π(12)(11) m2              

Thus, the area ofCanvas required for tent

S = S1 +S= (22/7 × 12 × 13) + (2 × 22/7 × 12 × 11)

S = 490 + 829.38

S = 1319.8 m2

S = 1320 m2

Therefore, the area ofcanvas required for the tent is 1320 m2

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